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Simplifying (2x + 1)(x + -1) = 90 Reorder the terms: (1 + 2x)(x + -1) = 90 Reorder the terms: (1 + 2x)(-1 + x) = 90 Multiply (1 + 2x) * (-1 + x) (1(-1 + x) + 2x * (-1 + x)) = 90 ((-1 * 1 + x * 1) + 2x * (-1 + x)) = 90 ((-1 + 1x) + 2x * (-1 + x)) = 90 (-1 + 1x + (-1 * 2x + x * 2x)) = 90 (-1 + 1x + (-2x + 2x2)) = 90 Combine like terms: 1x + -2x = -1x (-1 + -1x + 2x2) = 90 Solving -1 + -1x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -1 + -90 + -1x + 2x2 = 90 + -90 Combine like terms: -1 + -90 = -91 -91 + -1x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -91 + -1x + 2x2 = 0 Factor a trinomial. (-13 + -2x)(7 + -1x) = 0Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve: Simplifying -13 + -2x = 0 Solving -13 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2x = 0 + 13 -2x = 0 + 13 Combine like terms: 0 + 13 = 13 -2x = 13 Divide each side by '-2'. x = -6.5 Simplifying x = -6.5Subproblem 2
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 = 7Solution
x = {-6.5, 7}
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