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Simplifying 2(x + 3)(x + 3) + -5 = 14x + 17 Reorder the terms: 2(3 + x)(x + 3) + -5 = 14x + 17 Reorder the terms: 2(3 + x)(3 + x) + -5 = 14x + 17 Multiply (3 + x) * (3 + x) 2(3(3 + x) + x(3 + x)) + -5 = 14x + 17 2((3 * 3 + x * 3) + x(3 + x)) + -5 = 14x + 17 2((9 + 3x) + x(3 + x)) + -5 = 14x + 17 2(9 + 3x + (3 * x + x * x)) + -5 = 14x + 17 2(9 + 3x + (3x + x2)) + -5 = 14x + 17 Combine like terms: 3x + 3x = 6x 2(9 + 6x + x2) + -5 = 14x + 17 (9 * 2 + 6x * 2 + x2 * 2) + -5 = 14x + 17 (18 + 12x + 2x2) + -5 = 14x + 17 Reorder the terms: 18 + -5 + 12x + 2x2 = 14x + 17 Combine like terms: 18 + -5 = 13 13 + 12x + 2x2 = 14x + 17 Reorder the terms: 13 + 12x + 2x2 = 17 + 14x Solving 13 + 12x + 2x2 = 17 + 14x Solving for variable 'x'. Reorder the terms: 13 + -17 + 12x + -14x + 2x2 = 17 + 14x + -17 + -14x Combine like terms: 13 + -17 = -4 -4 + 12x + -14x + 2x2 = 17 + 14x + -17 + -14x Combine like terms: 12x + -14x = -2x -4 + -2x + 2x2 = 17 + 14x + -17 + -14x Reorder the terms: -4 + -2x + 2x2 = 17 + -17 + 14x + -14x Combine like terms: 17 + -17 = 0 -4 + -2x + 2x2 = 0 + 14x + -14x -4 + -2x + 2x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -4 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -1x + x2) = 0 Factor a trinomial. 2((-1 + -1x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-1, 2}
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