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Simplifying 5x + 105 = (3x + 13)(3x + 13) Reorder the terms: 105 + 5x = (3x + 13)(3x + 13) Reorder the terms: 105 + 5x = (13 + 3x)(3x + 13) Reorder the terms: 105 + 5x = (13 + 3x)(13 + 3x) Multiply (13 + 3x) * (13 + 3x) 105 + 5x = (13(13 + 3x) + 3x * (13 + 3x)) 105 + 5x = ((13 * 13 + 3x * 13) + 3x * (13 + 3x)) 105 + 5x = ((169 + 39x) + 3x * (13 + 3x)) 105 + 5x = (169 + 39x + (13 * 3x + 3x * 3x)) 105 + 5x = (169 + 39x + (39x + 9x2)) Combine like terms: 39x + 39x = 78x 105 + 5x = (169 + 78x + 9x2) Solving 105 + 5x = 169 + 78x + 9x2 Solving for variable 'x'. Reorder the terms: 105 + -169 + 5x + -78x + -9x2 = 169 + 78x + 9x2 + -169 + -78x + -9x2 Combine like terms: 105 + -169 = -64 -64 + 5x + -78x + -9x2 = 169 + 78x + 9x2 + -169 + -78x + -9x2 Combine like terms: 5x + -78x = -73x -64 + -73x + -9x2 = 169 + 78x + 9x2 + -169 + -78x + -9x2 Reorder the terms: -64 + -73x + -9x2 = 169 + -169 + 78x + -78x + 9x2 + -9x2 Combine like terms: 169 + -169 = 0 -64 + -73x + -9x2 = 0 + 78x + -78x + 9x2 + -9x2 -64 + -73x + -9x2 = 78x + -78x + 9x2 + -9x2 Combine like terms: 78x + -78x = 0 -64 + -73x + -9x2 = 0 + 9x2 + -9x2 -64 + -73x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -64 + -73x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(64 + 73x + 9x2) = 0 Factor a trinomial. -1((64 + 9x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(64 + 9x)' equal to zero and attempt to solve: Simplifying 64 + 9x = 0 Solving 64 + 9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -64 + 9x = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 9x = 0 + -64 9x = 0 + -64 Combine like terms: 0 + -64 = -64 9x = -64 Divide each side by '9'. x = -7.111111111 Simplifying x = -7.111111111Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-7.111111111, -1}
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