SOLUTION: i'm in pre-calculus and our teacher gave us an extra credit problem. It reads: Derive the quadratic formula. (Hint: Solve the general quadratic equation ax^2+bx+c=0 but a cann

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: i'm in pre-calculus and our teacher gave us an extra credit problem. It reads: Derive the quadratic formula. (Hint: Solve the general quadratic equation ax^2+bx+c=0 but a cann      Log On

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Question 14211: i'm in pre-calculus and our teacher gave us an extra credit problem. It reads:
Derive the quadratic formula. (Hint: Solve the general quadratic equation ax^2+bx+c=0 but a cannot = 0)
How do i go about solving this? I need it for tomorrow. 10/7/05

thanks!!
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Try this:
ax%5E2+%2B+bx+%2B+c+=+0 Divide both sides by a.
x%5E2+%2B+%28b%2Fa%29x+%2B+c%2Fa+=+0 Subtract c/a from both sides.
x%5E2+%2B+%28b%2Fa%29x+=+-c%2Fa Now "complete the square" in x on the left side.
x%5E2+%2B+%28b%2Fa%29x+%2B+%28b%2F2a%29%5E2+=+%28b%2F2a%29%5E2+-+c%2Fa Factor the left side.
%28x+%2B+b%2F2a%29%5E2+=+%28b%2F2a%29%5E2+-+c%2Fa Simplify the right side and take the square root of both sides.
x+%2B+b%2F2a+=+%2B-sqrt%28b%5E2%2F4a%5E2+-+c%2Fa%29 Simplify the radical.
x+%2B+b%2F2a+=+%2B-sqrt%28%28b%5E2+-+4ac%29%2F4a%5E2%29 Subtract b/2a from both sides.
x+=+-b%2F2a+%2B-sqrt%28b%5E2+-+4ac%29%2F2a Simplify.
x+=+%28-b%2B-sqrt%28b%5E2+-+4ac%29%29%2F2a Does this look familiar?