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Simplifying x2 + (13 + -1x)(13 + -1x) = 85 Multiply (13 + -1x) * (13 + -1x) x2 + (13(13 + -1x) + -1x * (13 + -1x)) = 85 x2 + ((13 * 13 + -1x * 13) + -1x * (13 + -1x)) = 85 x2 + ((169 + -13x) + -1x * (13 + -1x)) = 85 x2 + (169 + -13x + (13 * -1x + -1x * -1x)) = 85 x2 + (169 + -13x + (-13x + 1x2)) = 85 Combine like terms: -13x + -13x = -26x x2 + (169 + -26x + 1x2) = 85 Reorder the terms: 169 + -26x + x2 + 1x2 = 85 Combine like terms: x2 + 1x2 = 2x2 169 + -26x + 2x2 = 85 Solving 169 + -26x + 2x2 = 85 Solving for variable 'x'. Reorder the terms: 169 + -85 + -26x + 2x2 = 85 + -85 Combine like terms: 169 + -85 = 84 84 + -26x + 2x2 = 85 + -85 Combine like terms: 85 + -85 = 0 84 + -26x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(42 + -13x + x2) = 0 Factor a trinomial. 2((6 + -1x)(7 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {6, 7}
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