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Simplifying 5x2 + 5x + -1 = -1x2 + 4x Reorder the terms: -1 + 5x + 5x2 = -1x2 + 4x Reorder the terms: -1 + 5x + 5x2 = 4x + -1x2 Solving -1 + 5x + 5x2 = 4x + -1x2 Solving for variable 'x'. Reorder the terms: -1 + 5x + -4x + 5x2 + x2 = 4x + -1x2 + -4x + x2 Combine like terms: 5x + -4x = 1x -1 + 1x + 5x2 + x2 = 4x + -1x2 + -4x + x2 Combine like terms: 5x2 + x2 = 6x2 -1 + 1x + 6x2 = 4x + -1x2 + -4x + x2 Reorder the terms: -1 + 1x + 6x2 = 4x + -4x + -1x2 + x2 Combine like terms: 4x + -4x = 0 -1 + 1x + 6x2 = 0 + -1x2 + x2 -1 + 1x + 6x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -1 + 1x + 6x2 = 0 Factor a trinomial. (-1 + -2x)(1 + -3x) = 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 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-0.5, 0.3333333333}
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