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Simplifying 4x2 = 1 + -3x Solving 4x2 = 1 + -3x Solving for variable 'x'. Reorder the terms: -1 + 3x + 4x2 = 1 + -3x + -1 + 3x Reorder the terms: -1 + 3x + 4x2 = 1 + -1 + -3x + 3x Combine like terms: 1 + -1 = 0 -1 + 3x + 4x2 = 0 + -3x + 3x -1 + 3x + 4x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -1 + 3x + 4x2 = 0 Factor a trinomial. (-1 + -1x)(1 + -4x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {-1, 0.25}
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