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Simplifying 40x2 = 27x + 7 Reorder the terms: 40x2 = 7 + 27x Solving 40x2 = 7 + 27x Solving for variable 'x'. Reorder the terms: -7 + -27x + 40x2 = 7 + 27x + -7 + -27x Reorder the terms: -7 + -27x + 40x2 = 7 + -7 + 27x + -27x Combine like terms: 7 + -7 = 0 -7 + -27x + 40x2 = 0 + 27x + -27x -7 + -27x + 40x2 = 27x + -27x Combine like terms: 27x + -27x = 0 -7 + -27x + 40x2 = 0 Factor a trinomial. (-1 + -5x)(7 + -8x) = 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 '(7 + -8x)' equal to zero and attempt to solve: Simplifying 7 + -8x = 0 Solving 7 + -8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -8x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8x = 0 + -7 -8x = 0 + -7 Combine like terms: 0 + -7 = -7 -8x = -7 Divide each side by '-8'. x = 0.875 Simplifying x = 0.875Solution
x = {-0.2, 0.875}
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