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Simplifying x2 + x(1 + -1x) + -1(1 + -1x)(1 + -1x) = -29 x2 + (1 * x + -1x * x) + -1(1 + -1x)(1 + -1x) = -29 x2 + (1x + -1x2) + -1(1 + -1x)(1 + -1x) = -29 Multiply (1 + -1x) * (1 + -1x) x2 + 1x + -1x2 + -1(1(1 + -1x) + -1x * (1 + -1x)) = -29 x2 + 1x + -1x2 + -1((1 * 1 + -1x * 1) + -1x * (1 + -1x)) = -29 x2 + 1x + -1x2 + -1((1 + -1x) + -1x * (1 + -1x)) = -29 x2 + 1x + -1x2 + -1(1 + -1x + (1 * -1x + -1x * -1x)) = -29 x2 + 1x + -1x2 + -1(1 + -1x + (-1x + 1x2)) = -29 Combine like terms: -1x + -1x = -2x x2 + 1x + -1x2 + -1(1 + -2x + 1x2) = -29 x2 + 1x + -1x2 + (1 * -1 + -2x * -1 + 1x2 * -1) = -29 x2 + 1x + -1x2 + (-1 + 2x + -1x2) = -29 Reorder the terms: -1 + 1x + 2x + x2 + -1x2 + -1x2 = -29 Combine like terms: 1x + 2x = 3x -1 + 3x + x2 + -1x2 + -1x2 = -29 Combine like terms: x2 + -1x2 = 0 -1 + 3x + 0 + -1x2 = -29 -1 + 3x + -1x2 = -29 Solving -1 + 3x + -1x2 = -29 Solving for variable 'x'. Reorder the terms: -1 + 29 + 3x + -1x2 = -29 + 29 Combine like terms: -1 + 29 = 28 28 + 3x + -1x2 = -29 + 29 Combine like terms: -29 + 29 = 0 28 + 3x + -1x2 = 0 Factor a trinomial. (7 + -1x)(4 + x) = 0Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {7, -4}
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