SOLUTION: What's are the steps to deriving a quadratic formula, and can you explain how you did each step?

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Question 428435: What's are the steps to deriving a quadratic formula, and can you explain how you did each step?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the general form ax%5E2+%2B+bx+%2B+c+=+0 and divide both sides by a to get x%5E2+%2B+%28b%2Fa%29x+%2B+%28c%2Fa%29+=+0. To complete the square, we want the constant term to be %28b%2F2a%29%5E2 or b%5E2%2F4a%5E2 so we add b%5E2%2F4a%5E2+-+c%2Fa to both sides to get

. The left side factors to %28x+-+b%2F2a%29%5E2 so the equation is equivalent to

%28x+%2B+b%2F2a%29%5E2+=+%28b%5E2+-+4ac%29%2F4a%5E2

Taking square root of both sides,

x+%2B+b%2F2a+=+%280+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a
x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a <-- and there's the quadratic formula.