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urp:poly [2022-01-07] nerf_herder [Completing the square] |
urp:poly [2022-01-07] nerf_herder |
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That becomes (x + b/2a)² = -c/a + (b/2a)² | That becomes (x + b/2a)² = -c/a + (b/2a)² | ||
Call d = b/2a: (x + d)² = d² - c/a | Call d = b/2a: (x + d)² = d² - c/a | ||
- | Take square roots: x + d = √(d² - c/a), and simplify | + | Take square roots: x + d = ±√(d² - c/a), and simplify |
+ | (This gives two answers, call it u and v. | ||
+ | The quadratic equation can then be rewritten as: a(x+u)(x+v) = 0) | ||
=== Method 2 === | === Method 2 === |