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Simplifying (6 + 2x)(12 + 2x) = 160 Multiply (6 + 2x) * (12 + 2x) (6(12 + 2x) + 2x * (12 + 2x)) = 160 ((12 * 6 + 2x * 6) + 2x * (12 + 2x)) = 160 ((72 + 12x) + 2x * (12 + 2x)) = 160 (72 + 12x + (12 * 2x + 2x * 2x)) = 160 (72 + 12x + (24x + 4x2)) = 160 Combine like terms: 12x + 24x = 36x (72 + 36x + 4x2) = 160 Solving 72 + 36x + 4x2 = 160 Solving for variable 'x'. Reorder the terms: 72 + -160 + 36x + 4x2 = 160 + -160 Combine like terms: 72 + -160 = -88 -88 + 36x + 4x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -88 + 36x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-22 + 9x + x2) = 0 Factor a trinomial. 4((-11 + -1x)(2 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve: Simplifying -11 + -1x = 0 Solving -11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x = 0 + 11 -1x = 0 + 11 Combine like terms: 0 + 11 = 11 -1x = 11 Divide each side by '-1'. x = -11 Simplifying x = -11Subproblem 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 = {-11, 2}
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