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Simplifying (x + -1)(x + -1) + -13(x + -1) + 36 = 0 Reorder the terms: (-1 + x)(x + -1) + -13(x + -1) + 36 = 0 Reorder the terms: (-1 + x)(-1 + x) + -13(x + -1) + 36 = 0 Multiply (-1 + x) * (-1 + x) (-1(-1 + x) + x(-1 + x)) + -13(x + -1) + 36 = 0 ((-1 * -1 + x * -1) + x(-1 + x)) + -13(x + -1) + 36 = 0 ((1 + -1x) + x(-1 + x)) + -13(x + -1) + 36 = 0 (1 + -1x + (-1 * x + x * x)) + -13(x + -1) + 36 = 0 (1 + -1x + (-1x + x2)) + -13(x + -1) + 36 = 0 Combine like terms: -1x + -1x = -2x (1 + -2x + x2) + -13(x + -1) + 36 = 0 Reorder the terms: 1 + -2x + x2 + -13(-1 + x) + 36 = 0 1 + -2x + x2 + (-1 * -13 + x * -13) + 36 = 0 1 + -2x + x2 + (13 + -13x) + 36 = 0 Reorder the terms: 1 + 13 + 36 + -2x + -13x + x2 = 0 Combine like terms: 1 + 13 = 14 14 + 36 + -2x + -13x + x2 = 0 Combine like terms: 14 + 36 = 50 50 + -2x + -13x + x2 = 0 Combine like terms: -2x + -13x = -15x 50 + -15x + x2 = 0 Solving 50 + -15x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (5 + -1x)(10 + -1x) = 0Subproblem 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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {5, 10}
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