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Simplifying (10 + 2x)(8 + 2x) = 120 Multiply (10 + 2x) * (8 + 2x) (10(8 + 2x) + 2x * (8 + 2x)) = 120 ((8 * 10 + 2x * 10) + 2x * (8 + 2x)) = 120 ((80 + 20x) + 2x * (8 + 2x)) = 120 (80 + 20x + (8 * 2x + 2x * 2x)) = 120 (80 + 20x + (16x + 4x2)) = 120 Combine like terms: 20x + 16x = 36x (80 + 36x + 4x2) = 120 Solving 80 + 36x + 4x2 = 120 Solving for variable 'x'. Reorder the terms: 80 + -120 + 36x + 4x2 = 120 + -120 Combine like terms: 80 + -120 = -40 -40 + 36x + 4x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -40 + 36x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + 9x + x2) = 0 Factor a trinomial. 4((-10 + -1x)(1 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve: Simplifying -10 + -1x = 0 Solving -10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1x = 0 + 10 -1x = 0 + 10 Combine like terms: 0 + 10 = 10 -1x = 10 Divide each side by '-1'. x = -10 Simplifying x = -10Subproblem 2
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 = 1Solution
x = {-10, 1}
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