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Simplifying (18 + -2x)(16 + -2x) = 168 Multiply (18 + -2x) * (16 + -2x) (18(16 + -2x) + -2x * (16 + -2x)) = 168 ((16 * 18 + -2x * 18) + -2x * (16 + -2x)) = 168 ((288 + -36x) + -2x * (16 + -2x)) = 168 (288 + -36x + (16 * -2x + -2x * -2x)) = 168 (288 + -36x + (-32x + 4x2)) = 168 Combine like terms: -36x + -32x = -68x (288 + -68x + 4x2) = 168 Solving 288 + -68x + 4x2 = 168 Solving for variable 'x'. Reorder the terms: 288 + -168 + -68x + 4x2 = 168 + -168 Combine like terms: 288 + -168 = 120 120 + -68x + 4x2 = 168 + -168 Combine like terms: 168 + -168 = 0 120 + -68x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(30 + -17x + x2) = 0 Factor a trinomial. 4((2 + -1x)(15 + -1x)) = 0 Ignore the factor 4.Subproblem 1
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 = 2Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {2, 15}
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