SOLUTION: Derive the quadratic formula by completing the square for: ax squared + bx + c = 0

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Question 31789: Derive the quadratic formula by completing the square for:
ax squared + bx + c = 0
Answer by Earlsdon(6103) About Me  (Show Source):
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ax%5E2+%2B+bx+%2B+c+=+0 Subtract c from both sides of the equation.
ax%5E2+%2B+bx+=+-c Divide both sides by a.
x%5E2+%2B+%28b%2Fa%29x+=+%28-c%2Fa%29 Complete the square in the x-terms by adding the square of half the x-coefficient %28b%2F2a%29%5E2+=+b%5E2%2F4a%5E2 to both sides.
x%5E2+%2B+%28b%2Fa%29x+%2B+b%5E2%2F4a%5E2+=+%28b%5E2%2F4a%5E2%29+-+c%2Fa Factor the left side of the equation.
%28x+%2B+%28b%2F2a%29%29%5E2+=+b%5E2%2F4a%5E2+-+c%2Fa Simplify the right side.
%28x+%2B+%28b%2F2a%29%29%5E2+=+%28b%5E2+-+4ac%29%2F4a%5E2 Take the square root of both sides.
%28x+%2B+%28b%2F2a%29%29+=+%28sqrt%28b%5E2+-+4ac%29%29%2F2a Subtractb%2F2a from both sides.
x+=+%28-b%2F2a%29+%2B-sqrt%28b%5E2+-+4ac%29%2F2a Simplify.
x+=+%28-b%2B-sqrt%28b%5E2+-+4ac%29%29%2F2a