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Simplifying -75x2 + 290x = 240 Reorder the terms: 290x + -75x2 = 240 Solving 290x + -75x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 290x + -75x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 290x + -75x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-48 + 58x + -15x2) = 0 Factor a trinomial. 5((-8 + 3x)(6 + -5x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-8 + 3x)' equal to zero and attempt to solve: Simplifying -8 + 3x = 0 Solving -8 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 3x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3x = 0 + 8 3x = 0 + 8 Combine like terms: 0 + 8 = 8 3x = 8 Divide each side by '3'. x = 2.666666667 Simplifying x = 2.666666667Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Divide each side by '-5'. x = 1.2 Simplifying x = 1.2Solution
x = {2.666666667, 1.2}
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