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Simplifying x(x + 2) + -1(x + 1) = 5(x + 2) + 1 Reorder the terms: x(2 + x) + -1(x + 1) = 5(x + 2) + 1 (2 * x + x * x) + -1(x + 1) = 5(x + 2) + 1 (2x + x2) + -1(x + 1) = 5(x + 2) + 1 Reorder the terms: 2x + x2 + -1(1 + x) = 5(x + 2) + 1 2x + x2 + (1 * -1 + x * -1) = 5(x + 2) + 1 2x + x2 + (-1 + -1x) = 5(x + 2) + 1 Reorder the terms: -1 + 2x + -1x + x2 = 5(x + 2) + 1 Combine like terms: 2x + -1x = 1x -1 + 1x + x2 = 5(x + 2) + 1 Reorder the terms: -1 + 1x + x2 = 5(2 + x) + 1 -1 + 1x + x2 = (2 * 5 + x * 5) + 1 -1 + 1x + x2 = (10 + 5x) + 1 Reorder the terms: -1 + 1x + x2 = 10 + 1 + 5x Combine like terms: 10 + 1 = 11 -1 + 1x + x2 = 11 + 5x Solving -1 + 1x + x2 = 11 + 5x Solving for variable 'x'. Reorder the terms: -1 + -11 + 1x + -5x + x2 = 11 + 5x + -11 + -5x Combine like terms: -1 + -11 = -12 -12 + 1x + -5x + x2 = 11 + 5x + -11 + -5x Combine like terms: 1x + -5x = -4x -12 + -4x + x2 = 11 + 5x + -11 + -5x Reorder the terms: -12 + -4x + x2 = 11 + -11 + 5x + -5x Combine like terms: 11 + -11 = 0 -12 + -4x + x2 = 0 + 5x + -5x -12 + -4x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -12 + -4x + x2 = 0 Factor a trinomial. (-2 + -1x)(6 + -1x) = 0Subproblem 1
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 = -2Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-2, 6}
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