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Simplifying 15x = -10x2 + 10 Reorder the terms: 15x = 10 + -10x2 Solving 15x = 10 + -10x2 Solving for variable 'x'. Reorder the terms: -10 + 15x + 10x2 = 10 + -10x2 + -10 + 10x2 Reorder the terms: -10 + 15x + 10x2 = 10 + -10 + -10x2 + 10x2 Combine like terms: 10 + -10 = 0 -10 + 15x + 10x2 = 0 + -10x2 + 10x2 -10 + 15x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 -10 + 15x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + 3x + 2x2) = 0 Factor a trinomial. 5((-2 + -1x)(1 + -2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
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 = 0.5Solution
x = {-2, 0.5}
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