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Simplifying (80 + 2x)(60 + x) = 9600 Multiply (80 + 2x) * (60 + x) (80(60 + x) + 2x * (60 + x)) = 9600 ((60 * 80 + x * 80) + 2x * (60 + x)) = 9600 ((4800 + 80x) + 2x * (60 + x)) = 9600 (4800 + 80x + (60 * 2x + x * 2x)) = 9600 (4800 + 80x + (120x + 2x2)) = 9600 Combine like terms: 80x + 120x = 200x (4800 + 200x + 2x2) = 9600 Solving 4800 + 200x + 2x2 = 9600 Solving for variable 'x'. Reorder the terms: 4800 + -9600 + 200x + 2x2 = 9600 + -9600 Combine like terms: 4800 + -9600 = -4800 -4800 + 200x + 2x2 = 9600 + -9600 Combine like terms: 9600 + -9600 = 0 -4800 + 200x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2400 + 100x + x2) = 0 Factor a trinomial. 2((-120 + -1x)(20 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-120 + -1x)' equal to zero and attempt to solve: Simplifying -120 + -1x = 0 Solving -120 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + -1x = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -1x = 0 + 120 -1x = 0 + 120 Combine like terms: 0 + 120 = 120 -1x = 120 Divide each side by '-1'. x = -120 Simplifying x = -120Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Solution
x = {-120, 20}
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