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Simplifying 180 = (2x + 13)(2x + 10) Reorder the terms: 180 = (13 + 2x)(2x + 10) Reorder the terms: 180 = (13 + 2x)(10 + 2x) Multiply (13 + 2x) * (10 + 2x) 180 = (13(10 + 2x) + 2x * (10 + 2x)) 180 = ((10 * 13 + 2x * 13) + 2x * (10 + 2x)) 180 = ((130 + 26x) + 2x * (10 + 2x)) 180 = (130 + 26x + (10 * 2x + 2x * 2x)) 180 = (130 + 26x + (20x + 4x2)) Combine like terms: 26x + 20x = 46x 180 = (130 + 46x + 4x2) Solving 180 = 130 + 46x + 4x2 Solving for variable 'x'. Combine like terms: 180 + -130 = 50 50 + -46x + -4x2 = 130 + 46x + 4x2 + -130 + -46x + -4x2 Reorder the terms: 50 + -46x + -4x2 = 130 + -130 + 46x + -46x + 4x2 + -4x2 Combine like terms: 130 + -130 = 0 50 + -46x + -4x2 = 0 + 46x + -46x + 4x2 + -4x2 50 + -46x + -4x2 = 46x + -46x + 4x2 + -4x2 Combine like terms: 46x + -46x = 0 50 + -46x + -4x2 = 0 + 4x2 + -4x2 50 + -46x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 50 + -46x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -23x + -2x2) = 0 Factor a trinomial. 2((1 + -1x)(25 + 2x)) = 0 Ignore the factor 2.Subproblem 1
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 = 1Subproblem 2
Set the factor '(25 + 2x)' equal to zero and attempt to solve: Simplifying 25 + 2x = 0 Solving 25 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 2x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 2x = 0 + -25 2x = 0 + -25 Combine like terms: 0 + -25 = -25 2x = -25 Divide each side by '2'. x = -12.5 Simplifying x = -12.5Solution
x = {1, -12.5}
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