ax2+bx+c=0{\displaystyle ax^{2}+bx+c=0} The only condition is that a≠0,{\displaystyle a\neq 0,} because otherwise, the equation reduces to a linear equation. See if you can find general solutions for the special cases where b=0{\displaystyle b=0} and where c=0. {\displaystyle c=0. } ax2+bx=−c{\displaystyle ax^{2}+bx=-c} x2+bax=−ca{\displaystyle x^{2}+{\frac {b}{a}}x={\frac {-c}{a}}} x2+2b2ax+b24a2=b24a2−ca(x+b2a)2=b24a2−ca{\displaystyle {\begin{aligned}x^{2}+2{\frac {b}{2a}}x+{\frac {b^{2}}{4a^{2}}}&={\frac {b^{2}}{4a^{2}}}-{\frac {c}{a}}\\left(x+{\frac {b}{2a}}\right)^{2}&={\frac {b^{2}}{4a^{2}}}-{\frac {c}{a}}\end{aligned}}} Here, it is clear why a≠0,{\displaystyle a\neq 0,} since a{\displaystyle a} is in the denominator, and you cannot divide by 0....

Each year the American Institute of Architects singles out the nation’s Top Ten Green Projects, based on the incorporation of so-called sustainable design concepts. Is the project energy-efficient? Does it employ natural light and conserve water? Is the building designed to promote community interaction? In short, how does what we build have an impact on the world around us? Here, we spotlight four of 2006’s winners. A headquarters building is more than a roof over the head of the CEO; it’s a three-dimensional billboard advertising corporate values to the world....

Container gardens are a good option for someone who may want to rearrange their plants or eventually move them outdoors. Container gardens can grow any type of plant, in any size. Hydroponic gardens are a good option for someone who is looking to produce a lot of plants in a small amount of space. Typically, hydroponic gardens are used for growing vegetables. Avoid rooms that have cold temperatures (such as an attic or garage); cold can kill or slow the growth of your plants while heat is typically more universally welcomed by your plants....

It all started back on December 21, after a person on Twitter accused Baldwin of impersonating a Spanish person. That same Twitter user also shared a second post highlighting a video of Baldwin employing a Spanish accent during a live cooking segment on the Today show, and apparently forgetting the English word for cucumber. “Fake Spanish accent debut - this woman is from Massachusetts,” the tweet reads. More damning comments regarding Baldwin’s ethnicity emerged, including tweets from people alleging to be Baldwin’s former high school classmates in Boston who disputed claims that Baldwin made on her podcast in 2019 that she didn’t move to the United States until college....

The footage shows two sets of people crossing a street covered in water after heavy rainfall. In the month since it was first shared online by TikTok user @Rom2032, the video has been viewed over 7.9 million times. At first, two individuals, assumed by the poster to be millennials, but by many others online to be Gen Z, stood on the pavement by the crosswalk talking among themselves. The pair looked at the water as they talked, even stepping back at points and seemingly laughing....

The video, which has been viewed tens of millions of times across social media platforms, starts with a boy trying to pull out a sheep that had got stuck in a ditch. As the clip continues, the boy grabs the sheep by one of its back legs and carefully pulls it out until it is free. A sheep getting trapped is nothing unusual, but moments after it was freed the animal proved it may not have shared the same intelligence as other members of its flock....

Such is the case for a friend of Natalie Tyson, or @nat.tyson on TikTok. Last week, she shared her friend’s laughable online shopping experience that resulted in an alleged dress “violation.” Tyson begins her video with a text-to-speech video overlay, explaining to viewers that her “[sister’s] friend ordered a dress online.” She confirmed in a statement to Newsweek that the dress caught the eye of the unnamed friend looking for a cute outfit for her upcoming birthday....

My African-American friends and family encourage me to vote for Barack because he is extraordinary and different and a voice for change and oh, did they mention … black. As just one registered voter out of millions, why do I have to tell everyone I know who I am voting for? I cannot help but feel that my character hangs in the balance. If I vote for Hillary, I am turning my back on my race, or, worse, I’m a self-hating black....

Venturing up the East Coast, Hurricane Dorian brought heavy winds, rain and flooding to areas of South Carolina. As of Thursday morning, Dorian was a Category 3 hurricane on the Saffir-Simpson wind scale with maximum sustained winds of 115 miles-per-hour. The storm was located about 70 miles from Charleston, South Carolina, and throughout Thursday, the storm would move closer to the coast, according to the National Hurricane Center (NHC). Although Dorian didn’t make landfall, hurricane-force winds extended up to 60 miles from the center and tropical-storm-force winds reached even farther, up to 195 miles....

The Portland Police Bureau announced they responded to reports of a shooting at around 5:19 a.m. Authorities arrived to the scene and found two men dead: David Turner, who performed as 12 O’Clock, and Odion Turner, also known as Murdock. Cousins David Turner, 45, and Odion Turner, 50, were also cousins with the late Wu-Tang Clan member Ol’ Dirty Bastard, a.k.a. ODB. The Turners were members of the Brooklyn Zu, a group affiliated with ODB, and they both made a guest appearance on the track “Proteck Ya Neck II The Zoo” on ODB’s platinum-selling solo debut album, Return to the 36 Chambers: The Dirty Version,in 1995....

Wisconsin, a state hitherto best known for beer, cheese and the Green Bay Packers, may earn a place in history as the primary that finally tilted the race for the 2008 Democratic nomination to Barack Obama. In a decisive victory that showed just how dramatically Obama has cut into Hillary Clinton’s once-strong support among whites, women and blue-collar workers, the Illinois senator on Tuesday defeated his rival from New York 58 percent to 41 percent....

For years, non-white actors and activists have demanded better representation in television and film. Those pushing for change argue that far too often, white actors are cast to play Latinos. Sometimes, their skin is even darkened for the role. Actress Julissa Calderon, who stars in Gentefied on Netflix, is helping to lead the charge. “You’re sitting here and telling me that you are browning yourself up for a role, that millions of brown people already have that skin color, they could do it,” she told Good Morning America in a clip posted to Twitter on Thursday....

Plastic Surgery Began With Skin Grafts in Ancient India Physicians in ancient India used skin grafts for reconstructive surgery as early as 800 B.C. Later, in European countries, plastic surgery advances were slow in coming. However, eastern medicine took more readily to plastic surgery, and there are many recorded incidents of skin grafts and reconstructive surgery throughout history in that part of the world. Overall progress in plastic surgery, like most of medicine, was slow over the next few thousand years, as techniques used in India were introduced to the West and then subsequently refined and adapted for new applications....

Most everybody in the prediction business expected Philadelphia’s other rebuilding pro sports franchise (hi, Sixers) to have a better shot at losing 100 games than contending for a playoff spot this year. MORE: MLB Draft: Phillies on the clock, with plenty of options at No. 1 But here we are, with just a few days left in May, and only five NL teams have more wins than Philadelphia’s 26. And, though it’s obviously way too early to think about playoff positioning, it’s OK to mention that 26-21 record puts the Phillies only a game-and-a-half out of a wild-card spot entering play on Friday....

Personality disorders are further classified into one of three groups, including cluster A, cluster B, and cluster C. Histrionic personality disorder and narcissistic personality disorder are both cluster B personality disorders, and while there are similarities between these two conditions, there are some key differences. Learn more about what makes them different, why these differences are important, treatment options, and more. Differentiating Traits Since HPD and NPD are both cluster B personality disorders, they are similar....

Causes and Symptoms OHL is caused by the Epstein Barr virus (EBV), a virus of the herpes family that affects almost 95 percent of the population. While most people have an immune system able to control the virus, the diminished immune function in people with HIV provides OHL the opportunity to thrive. As such, it is considered an HIV-associated opportunistic infection. OHL lesions are benign and do not cause any other symptoms....

According to a paper published in the journal BMJ Case Reports, the HIV-positive recipient has adapted to the donation “without adverse events.” The world’s first living-donor HIV to HIV-kidney transplant was performed in the U.S. in 2019 at Johns Hopkins University. Organs are in great demand, with around 120,000 people around the U.S. waiting for a lifesaving transplant at any given time. Kidneys can be transplanted from living donors, as each person can function on a single kidney, which is a rare opportunity to save a life without the donor having to be dead....

Weight loss of at least 10% The presence of diarrhea or chronic weakness; Documented fever A duration of at least 30 days Not attributable to a concurrent condition other than HIV infection itself Wasting (cachexia) should not be confused with weight loss, the latter of which implies the loss of body weight. By contrast, wasting refers to the loss of body size and mass, most notably lean muscle mass. It is possible, for example, for someone with HIV to lose significant muscle mass while experiencing an increase in body fat....

At a safe house in a mainly Shiite suburb, the commander insisted, “We’re still in a state of war,” despite the ceasefire. He predicted new clashes, this time with the Christian forces of former warlord Samir Geagea, and said Hizbullah recently imported new arms, in preparation for the possible renewal of the 2006 border with Israel, though with new tactics—including better intelligence. Before leaving, the commander said quietly, “I’m being followed....

The 2022 Hlinka Gretzky Cup is ready for action, as some of the best U18 players in the world are gathered in Red Deer to play in the tournament. The annual competition features eight teams this season, including Canada, which did not compete during the 2021 edition. It is one of the first chances for members of the 2023 NHL Draft class to get their names out there on the international scale....