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Simplifying 2x + 19 = x2 + 16x + 64 Reorder the terms: 19 + 2x = x2 + 16x + 64 Reorder the terms: 19 + 2x = 64 + 16x + x2 Solving 19 + 2x = 64 + 16x + x2 Solving for variable 'x'. Reorder the terms: 19 + -64 + 2x + -16x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2 Combine like terms: 19 + -64 = -45 -45 + 2x + -16x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2 Combine like terms: 2x + -16x = -14x -45 + -14x + -1x2 = 64 + 16x + x2 + -64 + -16x + -1x2 Reorder the terms: -45 + -14x + -1x2 = 64 + -64 + 16x + -16x + x2 + -1x2 Combine like terms: 64 + -64 = 0 -45 + -14x + -1x2 = 0 + 16x + -16x + x2 + -1x2 -45 + -14x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 -45 + -14x + -1x2 = 0 + x2 + -1x2 -45 + -14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -45 + -14x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(45 + 14x + x2) = 0 Factor a trinomial. -1((9 + x)(5 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {-9, -5}
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