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Simplifying 2x2 + -2x + x + 1 = 4x + 1 Reorder the terms: 1 + -2x + x + 2x2 = 4x + 1 Combine like terms: -2x + x = -1x 1 + -1x + 2x2 = 4x + 1 Reorder the terms: 1 + -1x + 2x2 = 1 + 4x Add '-1' to each side of the equation. 1 + -1x + -1 + 2x2 = 1 + -1 + 4x Reorder the terms: 1 + -1 + -1x + 2x2 = 1 + -1 + 4x Combine like terms: 1 + -1 = 0 0 + -1x + 2x2 = 1 + -1 + 4x -1x + 2x2 = 1 + -1 + 4x Combine like terms: 1 + -1 = 0 -1x + 2x2 = 0 + 4x -1x + 2x2 = 4x Solving -1x + 2x2 = 4x Solving for variable 'x'. Reorder the terms: -1x + -4x + 2x2 = 4x + -4x Combine like terms: -1x + -4x = -5x -5x + 2x2 = 4x + -4x Combine like terms: 4x + -4x = 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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