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Simplifying (2x + 9)(x + 5) = (x + 9)(x + 4) Reorder the terms: (9 + 2x)(x + 5) = (x + 9)(x + 4) Reorder the terms: (9 + 2x)(5 + x) = (x + 9)(x + 4) Multiply (9 + 2x) * (5 + x) (9(5 + x) + 2x * (5 + x)) = (x + 9)(x + 4) ((5 * 9 + x * 9) + 2x * (5 + x)) = (x + 9)(x + 4) ((45 + 9x) + 2x * (5 + x)) = (x + 9)(x + 4) (45 + 9x + (5 * 2x + x * 2x)) = (x + 9)(x + 4) (45 + 9x + (10x + 2x2)) = (x + 9)(x + 4) Combine like terms: 9x + 10x = 19x (45 + 19x + 2x2) = (x + 9)(x + 4) Reorder the terms: 45 + 19x + 2x2 = (9 + x)(x + 4) Reorder the terms: 45 + 19x + 2x2 = (9 + x)(4 + x) Multiply (9 + x) * (4 + x) 45 + 19x + 2x2 = (9(4 + x) + x(4 + x)) 45 + 19x + 2x2 = ((4 * 9 + x * 9) + x(4 + x)) 45 + 19x + 2x2 = ((36 + 9x) + x(4 + x)) 45 + 19x + 2x2 = (36 + 9x + (4 * x + x * x)) 45 + 19x + 2x2 = (36 + 9x + (4x + x2)) Combine like terms: 9x + 4x = 13x 45 + 19x + 2x2 = (36 + 13x + x2) Solving 45 + 19x + 2x2 = 36 + 13x + x2 Solving for variable 'x'. Reorder the terms: 45 + -36 + 19x + -13x + 2x2 + -1x2 = 36 + 13x + x2 + -36 + -13x + -1x2 Combine like terms: 45 + -36 = 9 9 + 19x + -13x + 2x2 + -1x2 = 36 + 13x + x2 + -36 + -13x + -1x2 Combine like terms: 19x + -13x = 6x 9 + 6x + 2x2 + -1x2 = 36 + 13x + x2 + -36 + -13x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 9 + 6x + 1x2 = 36 + 13x + x2 + -36 + -13x + -1x2 Reorder the terms: 9 + 6x + 1x2 = 36 + -36 + 13x + -13x + x2 + -1x2 Combine like terms: 36 + -36 = 0 9 + 6x + 1x2 = 0 + 13x + -13x + x2 + -1x2 9 + 6x + 1x2 = 13x + -13x + x2 + -1x2 Combine like terms: 13x + -13x = 0 9 + 6x + 1x2 = 0 + x2 + -1x2 9 + 6x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 9 + 6x + 1x2 = 0 Factor a trinomial. (3 + x)(3 + x) = 0Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-3, -3}
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