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Simplifying 2((9 + 2x)(4 + x)) = 0 Multiply (9 + 2x) * (4 + x) 2((9(4 + x) + 2x * (4 + x))) = 0 2(((4 * 9 + x * 9) + 2x * (4 + x))) = 0 2(((36 + 9x) + 2x * (4 + x))) = 0 2((36 + 9x + (4 * 2x + x * 2x))) = 0 2((36 + 9x + (8x + 2x2))) = 0 Combine like terms: 9x + 8x = 17x 2((36 + 17x + 2x2)) = 0 (36 * 2 + 17x * 2 + 2x2 * 2) = 0 (72 + 34x + 4x2) = 0 Solving 72 + 34x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + 17x + 2x2) = 0 Factor a trinomial. 2((9 + 2x)(4 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 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 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-4.5, -4}
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