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Simplifying (30 + 2x)(24 + 2x) + -1(30 * 24) = 360 Multiply (30 + 2x) * (24 + 2x) (30(24 + 2x) + 2x * (24 + 2x)) + -1(30 * 24) = 360 ((24 * 30 + 2x * 30) + 2x * (24 + 2x)) + -1(30 * 24) = 360 ((720 + 60x) + 2x * (24 + 2x)) + -1(30 * 24) = 360 (720 + 60x + (24 * 2x + 2x * 2x)) + -1(30 * 24) = 360 (720 + 60x + (48x + 4x2)) + -1(30 * 24) = 360 Combine like terms: 60x + 48x = 108x (720 + 108x + 4x2) + -1(30 * 24) = 360 Multiply 30 * 24 720 + 108x + 4x2 + -1(720) = 360 Multiply -1 * 720 720 + 108x + 4x2 + -720 = 360 Reorder the terms: 720 + -720 + 108x + 4x2 = 360 Combine like terms: 720 + -720 = 0 0 + 108x + 4x2 = 360 108x + 4x2 = 360 Solving 108x + 4x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 108x + 4x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 108x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-90 + 27x + x2) = 0 Factor a trinomial. 4((-30 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-30 + -1x)' equal to zero and attempt to solve: Simplifying -30 + -1x = 0 Solving -30 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + -1x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -1x = 0 + 30 -1x = 0 + 30 Combine like terms: 0 + 30 = 30 -1x = 30 Divide each side by '-1'. x = -30 Simplifying x = -30Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-30, 3}
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