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Simplifying 13(x + -1)(x + -1) + -10(x + -1) + -3 = 0 Reorder the terms: 13(-1 + x)(x + -1) + -10(x + -1) + -3 = 0 Reorder the terms: 13(-1 + x)(-1 + x) + -10(x + -1) + -3 = 0 Multiply (-1 + x) * (-1 + x) 13(-1(-1 + x) + x(-1 + x)) + -10(x + -1) + -3 = 0 13((-1 * -1 + x * -1) + x(-1 + x)) + -10(x + -1) + -3 = 0 13((1 + -1x) + x(-1 + x)) + -10(x + -1) + -3 = 0 13(1 + -1x + (-1 * x + x * x)) + -10(x + -1) + -3 = 0 13(1 + -1x + (-1x + x2)) + -10(x + -1) + -3 = 0 Combine like terms: -1x + -1x = -2x 13(1 + -2x + x2) + -10(x + -1) + -3 = 0 (1 * 13 + -2x * 13 + x2 * 13) + -10(x + -1) + -3 = 0 (13 + -26x + 13x2) + -10(x + -1) + -3 = 0 Reorder the terms: 13 + -26x + 13x2 + -10(-1 + x) + -3 = 0 13 + -26x + 13x2 + (-1 * -10 + x * -10) + -3 = 0 13 + -26x + 13x2 + (10 + -10x) + -3 = 0 Reorder the terms: 13 + 10 + -3 + -26x + -10x + 13x2 = 0 Combine like terms: 13 + 10 = 23 23 + -3 + -26x + -10x + 13x2 = 0 Combine like terms: 23 + -3 = 20 20 + -26x + -10x + 13x2 = 0 Combine like terms: -26x + -10x = -36x 20 + -36x + 13x2 = 0 Solving 20 + -36x + 13x2 = 0 Solving for variable 'x'. Factor a trinomial. (10 + -13x)(2 + -1x) = 0Subproblem 1
Set the factor '(10 + -13x)' equal to zero and attempt to solve: Simplifying 10 + -13x = 0 Solving 10 + -13x = 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 + -13x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -13x = 0 + -10 -13x = 0 + -10 Combine like terms: 0 + -10 = -10 -13x = -10 Divide each side by '-13'. x = 0.7692307692 Simplifying x = 0.7692307692Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0.7692307692, 2}
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