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Simplifying 13x + 7x2 = 5x2 + 8x Reorder the terms: 13x + 7x2 = 8x + 5x2 Solving 13x + 7x2 = 8x + 5x2 Solving for variable 'x'. Reorder the terms: 13x + -8x + 7x2 + -5x2 = 8x + 5x2 + -8x + -5x2 Combine like terms: 13x + -8x = 5x 5x + 7x2 + -5x2 = 8x + 5x2 + -8x + -5x2 Combine like terms: 7x2 + -5x2 = 2x2 5x + 2x2 = 8x + 5x2 + -8x + -5x2 Reorder the terms: 5x + 2x2 = 8x + -8x + 5x2 + -5x2 Combine like terms: 8x + -8x = 0 5x + 2x2 = 0 + 5x2 + -5x2 5x + 2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 5x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 2x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = {0, -2.5}
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