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Simplifying 10x2 + 30x = -2x2 + -30x + -75 Reorder the terms: 30x + 10x2 = -2x2 + -30x + -75 Reorder the terms: 30x + 10x2 = -75 + -30x + -2x2 Solving 30x + 10x2 = -75 + -30x + -2x2 Solving for variable 'x'. Reorder the terms: 75 + 30x + 30x + 10x2 + 2x2 = -75 + -30x + -2x2 + 75 + 30x + 2x2 Combine like terms: 30x + 30x = 60x 75 + 60x + 10x2 + 2x2 = -75 + -30x + -2x2 + 75 + 30x + 2x2 Combine like terms: 10x2 + 2x2 = 12x2 75 + 60x + 12x2 = -75 + -30x + -2x2 + 75 + 30x + 2x2 Reorder the terms: 75 + 60x + 12x2 = -75 + 75 + -30x + 30x + -2x2 + 2x2 Combine like terms: -75 + 75 = 0 75 + 60x + 12x2 = 0 + -30x + 30x + -2x2 + 2x2 75 + 60x + 12x2 = -30x + 30x + -2x2 + 2x2 Combine like terms: -30x + 30x = 0 75 + 60x + 12x2 = 0 + -2x2 + 2x2 75 + 60x + 12x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 75 + 60x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(25 + 20x + 4x2) = 0 Factor a trinomial. 3((5 + 2x)(5 + 2x)) = 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 + 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 = -2.5Solution
x = {-2.5, -2.5}
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