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Simplifying (x + 8)(x + 8) + 15(x + 8) + 54 = 0 Reorder the terms: (8 + x)(x + 8) + 15(x + 8) + 54 = 0 Reorder the terms: (8 + x)(8 + x) + 15(x + 8) + 54 = 0 Multiply (8 + x) * (8 + x) (8(8 + x) + x(8 + x)) + 15(x + 8) + 54 = 0 ((8 * 8 + x * 8) + x(8 + x)) + 15(x + 8) + 54 = 0 ((64 + 8x) + x(8 + x)) + 15(x + 8) + 54 = 0 (64 + 8x + (8 * x + x * x)) + 15(x + 8) + 54 = 0 (64 + 8x + (8x + x2)) + 15(x + 8) + 54 = 0 Combine like terms: 8x + 8x = 16x (64 + 16x + x2) + 15(x + 8) + 54 = 0 Reorder the terms: 64 + 16x + x2 + 15(8 + x) + 54 = 0 64 + 16x + x2 + (8 * 15 + x * 15) + 54 = 0 64 + 16x + x2 + (120 + 15x) + 54 = 0 Reorder the terms: 64 + 120 + 54 + 16x + 15x + x2 = 0 Combine like terms: 64 + 120 = 184 184 + 54 + 16x + 15x + x2 = 0 Combine like terms: 184 + 54 = 238 238 + 16x + 15x + x2 = 0 Combine like terms: 16x + 15x = 31x 238 + 31x + x2 = 0 Solving 238 + 31x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (17 + x)(14 + x) = 0Subproblem 1
Set the factor '(17 + x)' equal to zero and attempt to solve: Simplifying 17 + x = 0 Solving 17 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + x = 0 + -17 x = 0 + -17 Combine like terms: 0 + -17 = -17 x = -17 Simplifying x = -17Subproblem 2
Set the factor '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Simplifying x = -14Solution
x = {-17, -14}
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