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Simplifying 4x2 + -20x + 25 + x2 = x2 + 10x + 25 Reorder the terms: 25 + -20x + 4x2 + x2 = x2 + 10x + 25 Combine like terms: 4x2 + x2 = 5x2 25 + -20x + 5x2 = x2 + 10x + 25 Reorder the terms: 25 + -20x + 5x2 = 25 + 10x + x2 Add '-25' to each side of the equation. 25 + -20x + -25 + 5x2 = 25 + 10x + -25 + x2 Reorder the terms: 25 + -25 + -20x + 5x2 = 25 + 10x + -25 + x2 Combine like terms: 25 + -25 = 0 0 + -20x + 5x2 = 25 + 10x + -25 + x2 -20x + 5x2 = 25 + 10x + -25 + x2 Reorder the terms: -20x + 5x2 = 25 + -25 + 10x + x2 Combine like terms: 25 + -25 = 0 -20x + 5x2 = 0 + 10x + x2 -20x + 5x2 = 10x + x2 Solving -20x + 5x2 = 10x + x2 Solving for variable 'x'. Reorder the terms: -20x + -10x + 5x2 + -1x2 = 10x + x2 + -10x + -1x2 Combine like terms: -20x + -10x = -30x -30x + 5x2 + -1x2 = 10x + x2 + -10x + -1x2 Combine like terms: 5x2 + -1x2 = 4x2 -30x + 4x2 = 10x + x2 + -10x + -1x2 Reorder the terms: -30x + 4x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -30x + 4x2 = 0 + x2 + -1x2 -30x + 4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -30x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-15 + 2x) = 0 Ignore the factor 2.Subproblem 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 '(-15 + 2x)' equal to zero and attempt to solve: Simplifying -15 + 2x = 0 Solving -15 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 2x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 2x = 0 + 15 2x = 0 + 15 Combine like terms: 0 + 15 = 15 2x = 15 Divide each side by '2'. x = 7.5 Simplifying x = 7.5Solution
x = {0, 7.5}
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