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Simplifying (5 + -1x)(2x + -1) = 18x Reorder the terms: (5 + -1x)(-1 + 2x) = 18x Multiply (5 + -1x) * (-1 + 2x) (5(-1 + 2x) + -1x * (-1 + 2x)) = 18x ((-1 * 5 + 2x * 5) + -1x * (-1 + 2x)) = 18x ((-5 + 10x) + -1x * (-1 + 2x)) = 18x (-5 + 10x + (-1 * -1x + 2x * -1x)) = 18x (-5 + 10x + (1x + -2x2)) = 18x Combine like terms: 10x + 1x = 11x (-5 + 11x + -2x2) = 18x Solving -5 + 11x + -2x2 = 18x Solving for variable 'x'. Reorder the terms: -5 + 11x + -18x + -2x2 = 18x + -18x Combine like terms: 11x + -18x = -7x -5 + -7x + -2x2 = 18x + -18x Combine like terms: 18x + -18x = 0 -5 + -7x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 7x + 2x2) = 0 Factor a trinomial. -1((5 + 2x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-2.5, -1}
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