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Simplifying 45(x + -1)(x + -1) + -9(x + -1) + -2 = 0 Reorder the terms: 45(-1 + x)(x + -1) + -9(x + -1) + -2 = 0 Reorder the terms: 45(-1 + x)(-1 + x) + -9(x + -1) + -2 = 0 Multiply (-1 + x) * (-1 + x) 45(-1(-1 + x) + x(-1 + x)) + -9(x + -1) + -2 = 0 45((-1 * -1 + x * -1) + x(-1 + x)) + -9(x + -1) + -2 = 0 45((1 + -1x) + x(-1 + x)) + -9(x + -1) + -2 = 0 45(1 + -1x + (-1 * x + x * x)) + -9(x + -1) + -2 = 0 45(1 + -1x + (-1x + x2)) + -9(x + -1) + -2 = 0 Combine like terms: -1x + -1x = -2x 45(1 + -2x + x2) + -9(x + -1) + -2 = 0 (1 * 45 + -2x * 45 + x2 * 45) + -9(x + -1) + -2 = 0 (45 + -90x + 45x2) + -9(x + -1) + -2 = 0 Reorder the terms: 45 + -90x + 45x2 + -9(-1 + x) + -2 = 0 45 + -90x + 45x2 + (-1 * -9 + x * -9) + -2 = 0 45 + -90x + 45x2 + (9 + -9x) + -2 = 0 Reorder the terms: 45 + 9 + -2 + -90x + -9x + 45x2 = 0 Combine like terms: 45 + 9 = 54 54 + -2 + -90x + -9x + 45x2 = 0 Combine like terms: 54 + -2 = 52 52 + -90x + -9x + 45x2 = 0 Combine like terms: -90x + -9x = -99x 52 + -99x + 45x2 = 0 Solving 52 + -99x + 45x2 = 0 Solving for variable 'x'. Factor a trinomial. (13 + -15x)(4 + -3x) = 0Subproblem 1
Set the factor '(13 + -15x)' equal to zero and attempt to solve: Simplifying 13 + -15x = 0 Solving 13 + -15x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -15x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -15x = 0 + -13 -15x = 0 + -13 Combine like terms: 0 + -13 = -13 -15x = -13 Divide each side by '-15'. x = 0.8666666667 Simplifying x = 0.8666666667Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {0.8666666667, 1.333333333}
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