The Quadratic Formula (Math Lair)

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If you've taken high-school math, you probably know that the quadratic formula is a formula that can be used to solve any quadratic equation, but you may well have forgotten how to derive it (if you ever saw how). Here's how to derive the quadratic formula. Given an equation in the form ax² + bx + c = 0:

ax² + bx + c = 0
ax² + bx = −c
x² + b⁄ax = −c⁄a
Now, complete the square on the left-hand side:
x² + b⁄ax + (b⁄2a)² = (b⁄2a)² − c⁄a
(x + b⁄2a)² = b² − 4ac⁄4a²
x + b⁄2a = ±√b² − 4ac⁄2a
x = −b⁄2a ±√b² − 4ac⁄2a
x = −b ± √b² − 4ac⁄2a