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ax² + bx + c = 0
ax² + bx = – c
Divide through by a
x² + bx/a = – c/a
Half of b/a = b/2a
Square of it = b²/4a²
Add b²/4a² to both sides
x² + bx/a + b²/4a² = b²/4a² – c/a
(x + b/2a)² = (b² – 4ac)/4a²
x + b/2a = ±√[(b² – 4ac)/4a²] x + b/2a = [±√(b² – 4ac)]/2a
x + b/2a = ±[√(b² – 4ac)]/2a
x = – b/2a ± [√(b² – 4ac)]/2a
∴ x = [- b ± √(b² – 4ac)] /2a

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