Answer:
See below.
Step-by-step explanation:
ax^2 + bx + c = 0
a(x^2 + b/a x) + c = 0
Completing the square:
a [ (x + b/2a)^2 - b^2/4a^2] + c = 0
a[ (x + b/2a )]^2 - b^2 / 4a + c = 0
a[ (x + b/2a )]^2 = b^2 / 4a - c
Dividing both sides by a:
(x + b/2a )^2 = b^2/4a^2 - c/a
Taking square roots of both sides:
x + b/2a = +/- √ (b^2/ 4a^2 - c/a)
x + b/2a = +/- √ [ ( b^2 - 4ac) / 4a^2 )]
x + b/2a = +/- √ ( b^2 - 4ac) / 2a
Subtracting b/2a from both sides and converting the right side to one fraction:
x = [- b +/- √ ( b^2 - 4ac] / 2a.
