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Simplifying (13 + -1x)(x2 + 5) = (7 + -1x)(x2 + 20) Reorder the terms: (13 + -1x)(5 + x2) = (7 + -1x)(x2 + 20) Multiply (13 + -1x) * (5 + x2) (13(5 + x2) + -1x * (5 + x2)) = (7 + -1x)(x2 + 20) ((5 * 13 + x2 * 13) + -1x * (5 + x2)) = (7 + -1x)(x2 + 20) ((65 + 13x2) + -1x * (5 + x2)) = (7 + -1x)(x2 + 20) (65 + 13x2 + (5 * -1x + x2 * -1x)) = (7 + -1x)(x2 + 20) (65 + 13x2 + (-5x + -1x3)) = (7 + -1x)(x2 + 20) Reorder the terms: (65 + -5x + 13x2 + -1x3) = (7 + -1x)(x2 + 20) (65 + -5x + 13x2 + -1x3) = (7 + -1x)(x2 + 20) Reorder the terms: 65 + -5x + 13x2 + -1x3 = (7 + -1x)(20 + x2) Multiply (7 + -1x) * (20 + x2) 65 + -5x + 13x2 + -1x3 = (7(20 + x2) + -1x * (20 + x2)) 65 + -5x + 13x2 + -1x3 = ((20 * 7 + x2 * 7) + -1x * (20 + x2)) 65 + -5x + 13x2 + -1x3 = ((140 + 7x2) + -1x * (20 + x2)) 65 + -5x + 13x2 + -1x3 = (140 + 7x2 + (20 * -1x + x2 * -1x)) 65 + -5x + 13x2 + -1x3 = (140 + 7x2 + (-20x + -1x3)) Reorder the terms: 65 + -5x + 13x2 + -1x3 = (140 + -20x + 7x2 + -1x3) 65 + -5x + 13x2 + -1x3 = (140 + -20x + 7x2 + -1x3) Add 'x3' to each side of the equation. 65 + -5x + 13x2 + -1x3 + x3 = 140 + -20x + 7x2 + -1x3 + x3 Combine like terms: -1x3 + x3 = 0 65 + -5x + 13x2 + 0 = 140 + -20x + 7x2 + -1x3 + x3 65 + -5x + 13x2 = 140 + -20x + 7x2 + -1x3 + x3 Combine like terms: -1x3 + x3 = 0 65 + -5x + 13x2 = 140 + -20x + 7x2 + 0 65 + -5x + 13x2 = 140 + -20x + 7x2 Solving 65 + -5x + 13x2 = 140 + -20x + 7x2 Solving for variable 'x'. Reorder the terms: 65 + -140 + -5x + 20x + 13x2 + -7x2 = 140 + -20x + 7x2 + -140 + 20x + -7x2 Combine like terms: 65 + -140 = -75 -75 + -5x + 20x + 13x2 + -7x2 = 140 + -20x + 7x2 + -140 + 20x + -7x2 Combine like terms: -5x + 20x = 15x -75 + 15x + 13x2 + -7x2 = 140 + -20x + 7x2 + -140 + 20x + -7x2 Combine like terms: 13x2 + -7x2 = 6x2 -75 + 15x + 6x2 = 140 + -20x + 7x2 + -140 + 20x + -7x2 Reorder the terms: -75 + 15x + 6x2 = 140 + -140 + -20x + 20x + 7x2 + -7x2 Combine like terms: 140 + -140 = 0 -75 + 15x + 6x2 = 0 + -20x + 20x + 7x2 + -7x2 -75 + 15x + 6x2 = -20x + 20x + 7x2 + -7x2 Combine like terms: -20x + 20x = 0 -75 + 15x + 6x2 = 0 + 7x2 + -7x2 -75 + 15x + 6x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -75 + 15x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-25 + 5x + 2x2) = 0 Factor a trinomial. 3((-5 + -1x)(5 + -2x)) = 0 Ignore the factor 3.Subproblem 1
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 = -5Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-5, 2.5}
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