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Simplifying 13x2 + 15 = 8x2 + 20x Reorder the terms: 15 + 13x2 = 8x2 + 20x Reorder the terms: 15 + 13x2 = 20x + 8x2 Solving 15 + 13x2 = 20x + 8x2 Solving for variable 'x'. Reorder the terms: 15 + -20x + 13x2 + -8x2 = 20x + 8x2 + -20x + -8x2 Combine like terms: 13x2 + -8x2 = 5x2 15 + -20x + 5x2 = 20x + 8x2 + -20x + -8x2 Reorder the terms: 15 + -20x + 5x2 = 20x + -20x + 8x2 + -8x2 Combine like terms: 20x + -20x = 0 15 + -20x + 5x2 = 0 + 8x2 + -8x2 15 + -20x + 5x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 15 + -20x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -4x + x2) = 0 Factor a trinomial. 5((1 + -1x)(3 + -1x)) = 0 Ignore the factor 5.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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {1, 3}
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