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Simplifying (5 + -2x)(1 + -1x) = 9 Multiply (5 + -2x) * (1 + -1x) (5(1 + -1x) + -2x * (1 + -1x)) = 9 ((1 * 5 + -1x * 5) + -2x * (1 + -1x)) = 9 ((5 + -5x) + -2x * (1 + -1x)) = 9 (5 + -5x + (1 * -2x + -1x * -2x)) = 9 (5 + -5x + (-2x + 2x2)) = 9 Combine like terms: -5x + -2x = -7x (5 + -7x + 2x2) = 9 Solving 5 + -7x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: 5 + -9 + -7x + 2x2 = 9 + -9 Combine like terms: 5 + -9 = -4 -4 + -7x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -4 + -7x + 2x2 = 0 Factor a trinomial. (-1 + -2x)(4 + -1x) = 0Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-0.5, 4}
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