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Simplifying 8x2 + -13x = 3x2 + -1 + -7x Reorder the terms: -13x + 8x2 = 3x2 + -1 + -7x Reorder the terms: -13x + 8x2 = -1 + -7x + 3x2 Solving -13x + 8x2 = -1 + -7x + 3x2 Solving for variable 'x'. Reorder the terms: 1 + -13x + 7x + 8x2 + -3x2 = -1 + -7x + 3x2 + 1 + 7x + -3x2 Combine like terms: -13x + 7x = -6x 1 + -6x + 8x2 + -3x2 = -1 + -7x + 3x2 + 1 + 7x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 1 + -6x + 5x2 = -1 + -7x + 3x2 + 1 + 7x + -3x2 Reorder the terms: 1 + -6x + 5x2 = -1 + 1 + -7x + 7x + 3x2 + -3x2 Combine like terms: -1 + 1 = 0 1 + -6x + 5x2 = 0 + -7x + 7x + 3x2 + -3x2 1 + -6x + 5x2 = -7x + 7x + 3x2 + -3x2 Combine like terms: -7x + 7x = 0 1 + -6x + 5x2 = 0 + 3x2 + -3x2 1 + -6x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 1 + -6x + 5x2 = 0 Factor a trinomial. (1 + -5x)(1 + -1x) = 0Subproblem 1
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 = 0.2Subproblem 2
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 = 1Solution
x = {0.2, 1}
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