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Simplifying -1x2 + 1 = -5x2 + 4x Reorder the terms: 1 + -1x2 = -5x2 + 4x Reorder the terms: 1 + -1x2 = 4x + -5x2 Solving 1 + -1x2 = 4x + -5x2 Solving for variable 'x'. Reorder the terms: 1 + -4x + -1x2 + 5x2 = 4x + -5x2 + -4x + 5x2 Combine like terms: -1x2 + 5x2 = 4x2 1 + -4x + 4x2 = 4x + -5x2 + -4x + 5x2 Reorder the terms: 1 + -4x + 4x2 = 4x + -4x + -5x2 + 5x2 Combine like terms: 4x + -4x = 0 1 + -4x + 4x2 = 0 + -5x2 + 5x2 1 + -4x + 4x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 1 + -4x + 4x2 = 0 Factor a trinomial. (1 + -2x)(1 + -2x) = 0Subproblem 1
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 = 0.5Subproblem 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 = {0.5, 0.5}
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