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Simplifying x(8x + 1) = 3x2 + -3x + 1 Reorder the terms: x(1 + 8x) = 3x2 + -3x + 1 (1 * x + 8x * x) = 3x2 + -3x + 1 (1x + 8x2) = 3x2 + -3x + 1 Reorder the terms: 1x + 8x2 = 1 + -3x + 3x2 Solving 1x + 8x2 = 1 + -3x + 3x2 Solving for variable 'x'. Reorder the terms: -1 + 1x + 3x + 8x2 + -3x2 = 1 + -3x + 3x2 + -1 + 3x + -3x2 Combine like terms: 1x + 3x = 4x -1 + 4x + 8x2 + -3x2 = 1 + -3x + 3x2 + -1 + 3x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 -1 + 4x + 5x2 = 1 + -3x + 3x2 + -1 + 3x + -3x2 Reorder the terms: -1 + 4x + 5x2 = 1 + -1 + -3x + 3x + 3x2 + -3x2 Combine like terms: 1 + -1 = 0 -1 + 4x + 5x2 = 0 + -3x + 3x + 3x2 + -3x2 -1 + 4x + 5x2 = -3x + 3x + 3x2 + -3x2 Combine like terms: -3x + 3x = 0 -1 + 4x + 5x2 = 0 + 3x2 + -3x2 -1 + 4x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -1 + 4x + 5x2 = 0 Factor a trinomial. (-1 + -1x)(1 + -5x) = 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 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Solution
x = {-1, 0.2}
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