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Simplifying (6 + -1x)(x + 6) + -1(x + -11) * x = 6 Reorder the terms: (6 + -1x)(6 + x) + -1(x + -11) * x = 6 Multiply (6 + -1x) * (6 + x) (6(6 + x) + -1x * (6 + x)) + -1(x + -11) * x = 6 ((6 * 6 + x * 6) + -1x * (6 + x)) + -1(x + -11) * x = 6 ((36 + 6x) + -1x * (6 + x)) + -1(x + -11) * x = 6 (36 + 6x + (6 * -1x + x * -1x)) + -1(x + -11) * x = 6 (36 + 6x + (-6x + -1x2)) + -1(x + -11) * x = 6 Combine like terms: 6x + -6x = 0 (36 + 0 + -1x2) + -1(x + -11) * x = 6 (36 + -1x2) + -1(x + -11) * x = 6 Reorder the terms: 36 + -1x2 + -1(-11 + x) * x = 6 Reorder the terms for easier multiplication: 36 + -1x2 + -1x(-11 + x) = 6 36 + -1x2 + (-11 * -1x + x * -1x) = 6 36 + -1x2 + (11x + -1x2) = 6 Reorder the terms: 36 + 11x + -1x2 + -1x2 = 6 Combine like terms: -1x2 + -1x2 = -2x2 36 + 11x + -2x2 = 6 Solving 36 + 11x + -2x2 = 6 Solving for variable 'x'. Reorder the terms: 36 + -6 + 11x + -2x2 = 6 + -6 Combine like terms: 36 + -6 = 30 30 + 11x + -2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 30 + 11x + -2x2 = 0 Factor a trinomial. (15 + -2x)(2 + x) = 0Subproblem 1
Set the factor '(15 + -2x)' equal to zero and attempt to solve: Simplifying 15 + -2x = 0 Solving 15 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -2x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -2x = 0 + -15 -2x = 0 + -15 Combine like terms: 0 + -15 = -15 -2x = -15 Divide each side by '-2'. x = 7.5 Simplifying x = 7.5Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {7.5, -2}
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