Algebra question (Will award best answer)?

Multiply both sides by 2a
2ax = -b ± √(b^2 - 4ac)

Add b to both sides
2ax + b = ±√(b^2 - 4ac)

Square both sides
(2ax + b)(2ax + b) = b^2 - 4ac

FOIL it out
4a^2x^2 + 4abx + b^2 = b^2 - 4ac

Subtract b^2 from both sides
4a^2x^2 + 4abx = -4ac

Move the 4a^2x^2 over by subtracting it from both sides
4abx = -4ac - 4a^2 x^2

Divide both sides by 4a
bx = -c - ax^2 and then divide both sides by x

x = [-b ± √(b² - 4ac)]/2a
2ax = -b ± √(b² - 4ac)
2ax + b = ± √(b² - 4ac)
[2ax + b]² = [± √(b² - 4ac)]²
4a²x² + 4abx + b² = b² - 4ac
4a²x² + 4abx = -4ac
4abx = -4ac - 4a²x²
bx = -c - ax²
bx = -(ax² + c)
b = -(ax² + c)/x


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A simpler way is to start from the quadratic equation.
ax² + bx + c = 0
bx = -(ax² + c)
b = -(ax² + c)/x