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Simplifying (8x + 1)(x + 2) = 13 + -1x Reorder the terms: (1 + 8x)(x + 2) = 13 + -1x Reorder the terms: (1 + 8x)(2 + x) = 13 + -1x Multiply (1 + 8x) * (2 + x) (1(2 + x) + 8x * (2 + x)) = 13 + -1x ((2 * 1 + x * 1) + 8x * (2 + x)) = 13 + -1x ((2 + 1x) + 8x * (2 + x)) = 13 + -1x (2 + 1x + (2 * 8x + x * 8x)) = 13 + -1x (2 + 1x + (16x + 8x2)) = 13 + -1x Combine like terms: 1x + 16x = 17x (2 + 17x + 8x2) = 13 + -1x Solving 2 + 17x + 8x2 = 13 + -1x Solving for variable 'x'. Reorder the terms: 2 + -13 + 17x + x + 8x2 = 13 + -1x + -13 + x Combine like terms: 2 + -13 = -11 -11 + 17x + x + 8x2 = 13 + -1x + -13 + x Combine like terms: 17x + x = 18x -11 + 18x + 8x2 = 13 + -1x + -13 + x Reorder the terms: -11 + 18x + 8x2 = 13 + -13 + -1x + x Combine like terms: 13 + -13 = 0 -11 + 18x + 8x2 = 0 + -1x + x -11 + 18x + 8x2 = -1x + x Combine like terms: -1x + x = 0 -11 + 18x + 8x2 = 0 Factor a trinomial. (-11 + -4x)(1 + -2x) = 0Subproblem 1
Set the factor '(-11 + -4x)' equal to zero and attempt to solve: Simplifying -11 + -4x = 0 Solving -11 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -4x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -4x = 0 + 11 -4x = 0 + 11 Combine like terms: 0 + 11 = 11 -4x = 11 Divide each side by '-4'. x = -2.75 Simplifying x = -2.75Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-2.75, 0.5}
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