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Simplifying (m + -12)(m + -12) = 225 Reorder the terms: (-12 + m)(m + -12) = 225 Reorder the terms: (-12 + m)(-12 + m) = 225 Multiply (-12 + m) * (-12 + m) (-12(-12 + m) + m(-12 + m)) = 225 ((-12 * -12 + m * -12) + m(-12 + m)) = 225 ((144 + -12m) + m(-12 + m)) = 225 (144 + -12m + (-12 * m + m * m)) = 225 (144 + -12m + (-12m + m2)) = 225 Combine like terms: -12m + -12m = -24m (144 + -24m + m2) = 225 Solving 144 + -24m + m2 = 225 Solving for variable 'm'. Reorder the terms: 144 + -225 + -24m + m2 = 225 + -225 Combine like terms: 144 + -225 = -81 -81 + -24m + m2 = 225 + -225 Combine like terms: 225 + -225 = 0 -81 + -24m + m2 = 0 Factor a trinomial. (-3 + -1m)(27 + -1m) = 0Subproblem 1
Set the factor '(-3 + -1m)' equal to zero and attempt to solve: Simplifying -3 + -1m = 0 Solving -3 + -1m = 0 Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1m = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1m = 0 + 3 -1m = 0 + 3 Combine like terms: 0 + 3 = 3 -1m = 3 Divide each side by '-1'. m = -3 Simplifying m = -3Subproblem 2
Set the factor '(27 + -1m)' equal to zero and attempt to solve: Simplifying 27 + -1m = 0 Solving 27 + -1m = 0 Move all terms containing m to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -1m = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1m = 0 + -27 -1m = 0 + -27 Combine like terms: 0 + -27 = -27 -1m = -27 Divide each side by '-1'. m = 27 Simplifying m = 27Solution
m = {-3, 27}
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