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Simplifying 8x2 + -7x = 4x + -14x2 Reorder the terms: -7x + 8x2 = 4x + -14x2 Solving -7x + 8x2 = 4x + -14x2 Solving for variable 'x'. Reorder the terms: -7x + -4x + 8x2 + 14x2 = 4x + -14x2 + -4x + 14x2 Combine like terms: -7x + -4x = -11x -11x + 8x2 + 14x2 = 4x + -14x2 + -4x + 14x2 Combine like terms: 8x2 + 14x2 = 22x2 -11x + 22x2 = 4x + -14x2 + -4x + 14x2 Reorder the terms: -11x + 22x2 = 4x + -4x + -14x2 + 14x2 Combine like terms: 4x + -4x = 0 -11x + 22x2 = 0 + -14x2 + 14x2 -11x + 22x2 = -14x2 + 14x2 Combine like terms: -14x2 + 14x2 = 0 -11x + 22x2 = 0 Factor out the Greatest Common Factor (GCF), '11x'. 11x(-1 + 2x) = 0 Ignore the factor 11.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 '(-1 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 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 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Divide each side by '2'. x = 0.5 Simplifying x = 0.5Solution
x = {0, 0.5}
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