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Simplifying 6x2 = 75 + 15x Solving 6x2 = 75 + 15x Solving for variable 'x'. Reorder the terms: -75 + -15x + 6x2 = 75 + 15x + -75 + -15x Reorder the terms: -75 + -15x + 6x2 = 75 + -75 + 15x + -15x Combine like terms: 75 + -75 = 0 -75 + -15x + 6x2 = 0 + 15x + -15x -75 + -15x + 6x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -75 + -15x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-25 + -5x + 2x2) = 0 Factor a trinomial. 3((-5 + -2x)(5 + -1x)) = 0 Ignore the factor 3.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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-2.5, 5}
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