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Simplifying (3x + -11)(5x + -4) = (x + 2)(-1x + 17) Reorder the terms: (-11 + 3x)(5x + -4) = (x + 2)(-1x + 17) Reorder the terms: (-11 + 3x)(-4 + 5x) = (x + 2)(-1x + 17) Multiply (-11 + 3x) * (-4 + 5x) (-11(-4 + 5x) + 3x * (-4 + 5x)) = (x + 2)(-1x + 17) ((-4 * -11 + 5x * -11) + 3x * (-4 + 5x)) = (x + 2)(-1x + 17) ((44 + -55x) + 3x * (-4 + 5x)) = (x + 2)(-1x + 17) (44 + -55x + (-4 * 3x + 5x * 3x)) = (x + 2)(-1x + 17) (44 + -55x + (-12x + 15x2)) = (x + 2)(-1x + 17) Combine like terms: -55x + -12x = -67x (44 + -67x + 15x2) = (x + 2)(-1x + 17) Reorder the terms: 44 + -67x + 15x2 = (2 + x)(-1x + 17) Reorder the terms: 44 + -67x + 15x2 = (2 + x)(17 + -1x) Multiply (2 + x) * (17 + -1x) 44 + -67x + 15x2 = (2(17 + -1x) + x(17 + -1x)) 44 + -67x + 15x2 = ((17 * 2 + -1x * 2) + x(17 + -1x)) 44 + -67x + 15x2 = ((34 + -2x) + x(17 + -1x)) 44 + -67x + 15x2 = (34 + -2x + (17 * x + -1x * x)) 44 + -67x + 15x2 = (34 + -2x + (17x + -1x2)) Combine like terms: -2x + 17x = 15x 44 + -67x + 15x2 = (34 + 15x + -1x2) Solving 44 + -67x + 15x2 = 34 + 15x + -1x2 Solving for variable 'x'. Reorder the terms: 44 + -34 + -67x + -15x + 15x2 + x2 = 34 + 15x + -1x2 + -34 + -15x + x2 Combine like terms: 44 + -34 = 10 10 + -67x + -15x + 15x2 + x2 = 34 + 15x + -1x2 + -34 + -15x + x2 Combine like terms: -67x + -15x = -82x 10 + -82x + 15x2 + x2 = 34 + 15x + -1x2 + -34 + -15x + x2 Combine like terms: 15x2 + x2 = 16x2 10 + -82x + 16x2 = 34 + 15x + -1x2 + -34 + -15x + x2 Reorder the terms: 10 + -82x + 16x2 = 34 + -34 + 15x + -15x + -1x2 + x2 Combine like terms: 34 + -34 = 0 10 + -82x + 16x2 = 0 + 15x + -15x + -1x2 + x2 10 + -82x + 16x2 = 15x + -15x + -1x2 + x2 Combine like terms: 15x + -15x = 0 10 + -82x + 16x2 = 0 + -1x2 + x2 10 + -82x + 16x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 10 + -82x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -41x + 8x2) = 0 Factor a trinomial. 2((1 + -8x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -8x)' equal to zero and attempt to solve: Simplifying 1 + -8x = 0 Solving 1 + -8x = 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 + -8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8x = 0 + -1 -8x = 0 + -1 Combine like terms: 0 + -1 = -1 -8x = -1 Divide each side by '-8'. x = 0.125 Simplifying x = 0.125Subproblem 2
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 = 5Solution
x = {0.125, 5}
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