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Simplifying (10 + x)(12 + x) = 120 Multiply (10 + x) * (12 + x) (10(12 + x) + x(12 + x)) = 120 ((12 * 10 + x * 10) + x(12 + x)) = 120 ((120 + 10x) + x(12 + x)) = 120 (120 + 10x + (12 * x + x * x)) = 120 (120 + 10x + (12x + x2)) = 120 Combine like terms: 10x + 12x = 22x (120 + 22x + x2) = 120 Add '-120' to each side of the equation. 120 + 22x + -120 + x2 = 120 + -120 Reorder the terms: 120 + -120 + 22x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 0 + 22x + x2 = 120 + -120 22x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 22x + x2 = 0 Solving 22x + x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(22 + x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(22 + x)' equal to zero and attempt to solve: Simplifying 22 + x = 0 Solving 22 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 0 + -22 Combine like terms: 22 + -22 = 0 0 + x = 0 + -22 x = 0 + -22 Combine like terms: 0 + -22 = -22 x = -22 Simplifying x = -22Solution
x = {0, -22}
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