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Simplifying x(x + 5) = (x + 0.5) * 2x Reorder the terms: x(5 + x) = (x + 0.5) * 2x (5 * x + x * x) = (x + 0.5) * 2x (5x + x2) = (x + 0.5) * 2x Reorder the terms: 5x + x2 = (0.5 + x) * 2x Reorder the terms for easier multiplication: 5x + x2 = 2x(0.5 + x) 5x + x2 = (0.5 * 2x + x * 2x) 5x + x2 = (1x + 2x2) Solving 5x + x2 = 1x + 2x2 Solving for variable 'x'. Reorder the terms: 5x + -1x + x2 + -2x2 = 1x + 2x2 + -1x + -2x2 Combine like terms: 5x + -1x = 4x 4x + x2 + -2x2 = 1x + 2x2 + -1x + -2x2 Combine like terms: x2 + -2x2 = -1x2 4x + -1x2 = 1x + 2x2 + -1x + -2x2 Reorder the terms: 4x + -1x2 = 1x + -1x + 2x2 + -2x2 Combine like terms: 1x + -1x = 0 4x + -1x2 = 0 + 2x2 + -2x2 4x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 4x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -1x) = 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0, 4}
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