Video: Solving Quadratic Equations

Solve 7𝑥² + 12𝑥 + 2 = 0.

01:38

Video Transcript

Solve seven 𝑥 squared plus twelve 𝑥 plus two equals zero. So this time, 𝑎 is seven, 𝑏 is twelve, and 𝑐 is two. They’re all positive. So I can put those into the formula. And then I get negative twelve plus or minus the square root of twelve squared minus four times seven times two all over two times seven, just by plugging in 𝑎, 𝑏 and 𝑐 into that formula. Well twelve squared is a hundred and forty-four, and four times seven is twenty-eight, and twenty-eight times two is fifty-six, so we’re subtracting fifty-six from that.

And again, we’ve got two values. Either 𝑥 is equal to negative twelve plus root eighty-eight all over fourteen or 𝑥 is equal to negative twelve minus root eighty-eight all over fourteen. Now root eighty-eight turns out to be an irrational number. We can’t just find a nice easy integer square root for it. So typically, in these questions you would either give your answer in its simplest surd form, or you would round to a specific number of decimal places. So either 𝑥 is equal to negative six plus root twenty-two over seven, which is minus nought point one nine to two decimal places, or 𝑥 is equal to negative six take away root twenty-two all over seven which is equal to minus one point five three to two decimal places. So that was probably a more typical example of the sort of question you’d be asked to answer, where the original expression up here didn’t factor nicely, so we couldn’t come up with nice simple answers.

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