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Simplifying 2(1 + -1x)(2x + -5) = 0 Reorder the terms: 2(1 + -1x)(-5 + 2x) = 0 Multiply (1 + -1x) * (-5 + 2x) 2(1(-5 + 2x) + -1x * (-5 + 2x)) = 0 2((-5 * 1 + 2x * 1) + -1x * (-5 + 2x)) = 0 2((-5 + 2x) + -1x * (-5 + 2x)) = 0 2(-5 + 2x + (-5 * -1x + 2x * -1x)) = 0 2(-5 + 2x + (5x + -2x2)) = 0 Combine like terms: 2x + 5x = 7x 2(-5 + 7x + -2x2) = 0 (-5 * 2 + 7x * 2 + -2x2 * 2) = 0 (-10 + 14x + -4x2) = 0 Solving -10 + 14x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 7x + -2x2) = 0 Factor a trinomial. 2((-5 + 2x)(1 + -1x)) = 0 Ignore the factor 2.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 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {2.5, 1}
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