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Simplifying 0 = 10x2 + -25x + 15 Reorder the terms: 0 = 15 + -25x + 10x2 Solving 0 = 15 + -25x + 10x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + 25x + -10x2 = 15 + -25x + 10x2 + -15 + 25x + -10x2 Reorder the terms: -15 + 25x + -10x2 = 15 + -15 + -25x + 25x + 10x2 + -10x2 Combine like terms: 15 + -15 = 0 -15 + 25x + -10x2 = 0 + -25x + 25x + 10x2 + -10x2 -15 + 25x + -10x2 = -25x + 25x + 10x2 + -10x2 Combine like terms: -25x + 25x = 0 -15 + 25x + -10x2 = 0 + 10x2 + -10x2 -15 + 25x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -15 + 25x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + 5x + -2x2) = 0 Factor a trinomial. 5((-3 + 2x)(1 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5Subproblem 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 = {1.5, 1}
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