SOLUTION: I have an extra credit problem in my college algebra class. I need to solve for x from the standard quadratic equation ax^2 + bx + c=0 to end as a result as the quadratic formula

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Question 4159: I have an extra credit problem in my college algebra class.
I need to solve for x from the standard quadratic equation ax^2 + bx + c=0 to end as a result as the quadratic formula! Any advice?
Answer by raafatriad(1) About Me  (Show Source):
You can put this solution on YOUR website!
a%2Ax%5E2%2Bb%2Ax%2Bc=0
by complete square:
add and subtract b%5E2%2F%284%2Aa%29
a%2Ax%5E2%2Bb%2Ax%2Bc%2B%28b%5E2%2F%284%2Aa%29%29-%28b%5E2%2F%284%2Aa%29%29=0
Rewrite the equation
%28a%2Ax%5E2%2Bb%2Ax%2Bb%5E2%2F%284%2Aa%29%29-b%5E2%2F%284%2Aa%29%2Bc=0
Factor for a
a%2A%28x%5E2%2Bb%2Fa%2Ax%2Bb%5E2%2F%284%2Aa%5E2%29%29-b%5E2%2F%284%2Aa%29%2Bc=0
Factor the complete square %28x%5E2%2Bb%2Fa%2Ax%2Bb%5E2%2F%284%2Aa%5E2%29%29
%28x%5E2%2Bb%2Fa%2Ax%2Bb%5E2%2F%284%2Aa%5E2%29%29=%28x%2Bb%2F%282%2Aa%29%29%5E2
a%2A%28x%2Bb%2F%282%2Aa%29%29%5E2-b%5E2%2F%284%2Aa%29%2Bc=0
a%2A%28x%2Bb%2F%282%2Aa%29%29%5E2=b%5E2%2F%284%2Aa%29-c
a%2A%28x%2Bb%2F%282%2Aa%29%29%5E2=%28b%5E2-4%2Aa%2Ac%29%2F%284%2Aa%29
Multiply both sides by 1%2Fa
%28x%2B%28b%2F%282%2Aa%29%29%29%5E2=%28b%5E2-4%2Aa%2Ac%29%2F%284%2Aa%5E2%29
Take the square root for both sides
x%2Bb%2F%282%2Aa%29=sqrt%28%28b%5E2-4%2Aa%2Ac%29%2F%284%2Aa%5E2%29%29 or x%2Bb%2F%282%2Aa%29=-sqrt%28%28b%5E2-4%2Aa%2Ac%29%2F%284%2Aa%5E2%29%29
x=%28-b%29%2F%282%2Aa%29%2Bsqrt%28b%5E2-4%2Aa%2Ac%29%2F%282%2Aa%29 or x=%28-b%29%2F%282%2Aa%29-sqrt%28b%5E2-4%2Aa%2Ac%29%2F%282%2Aa%29
x=%28-b%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29