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Simplifying 0 = -5x2 + 15x + -10 Reorder the terms: 0 = -10 + 15x + -5x2 Solving 0 = -10 + 15x + -5x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + -15x + 5x2 = -10 + 15x + -5x2 + 10 + -15x + 5x2 Reorder the terms: 10 + -15x + 5x2 = -10 + 10 + 15x + -15x + -5x2 + 5x2 Combine like terms: -10 + 10 = 0 10 + -15x + 5x2 = 0 + 15x + -15x + -5x2 + 5x2 10 + -15x + 5x2 = 15x + -15x + -5x2 + 5x2 Combine like terms: 15x + -15x = 0 10 + -15x + 5x2 = 0 + -5x2 + 5x2 10 + -15x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 10 + -15x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -3x + x2) = 0 Factor a trinomial. 5((1 + -1x)(2 + -1x)) = 0 Ignore the factor 5.Subproblem 1
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 = 1Subproblem 2
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 = 2Solution
x = {1, 2}
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