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Simplifying (80 + 2x)(60 + 2x) + -1(80 * 60) = 1500 Multiply (80 + 2x) * (60 + 2x) (80(60 + 2x) + 2x * (60 + 2x)) + -1(80 * 60) = 1500 ((60 * 80 + 2x * 80) + 2x * (60 + 2x)) + -1(80 * 60) = 1500 ((4800 + 160x) + 2x * (60 + 2x)) + -1(80 * 60) = 1500 (4800 + 160x + (60 * 2x + 2x * 2x)) + -1(80 * 60) = 1500 (4800 + 160x + (120x + 4x2)) + -1(80 * 60) = 1500 Combine like terms: 160x + 120x = 280x (4800 + 280x + 4x2) + -1(80 * 60) = 1500 Multiply 80 * 60 4800 + 280x + 4x2 + -1(4800) = 1500 Multiply -1 * 4800 4800 + 280x + 4x2 + -4800 = 1500 Reorder the terms: 4800 + -4800 + 280x + 4x2 = 1500 Combine like terms: 4800 + -4800 = 0 0 + 280x + 4x2 = 1500 280x + 4x2 = 1500 Solving 280x + 4x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + 280x + 4x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + 280x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-375 + 70x + x2) = 0 Factor a trinomial. 4((-75 + -1x)(5 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-75 + -1x)' equal to zero and attempt to solve: Simplifying -75 + -1x = 0 Solving -75 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + -1x = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -1x = 0 + 75 -1x = 0 + 75 Combine like terms: 0 + 75 = 75 -1x = 75 Divide each side by '-1'. x = -75 Simplifying x = -75Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-75, 5}
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