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Simplifying 5x(3x + 5) = 10 Reorder the terms: 5x(5 + 3x) = 10 (5 * 5x + 3x * 5x) = 10 (25x + 15x2) = 10 Solving 25x + 15x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 25x + 15x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 25x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + 5x + 3x2) = 0 Factor a trinomial. 5((-2 + -1x)(1 + -3x)) = 0 Ignore the factor 5.Subproblem 1
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 = -2Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-2, 0.3333333333}
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