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Simplifying 27x2 + -37x + 2 = 2x2 + 3x + -5 Reorder the terms: 2 + -37x + 27x2 = 2x2 + 3x + -5 Reorder the terms: 2 + -37x + 27x2 = -5 + 3x + 2x2 Solving 2 + -37x + 27x2 = -5 + 3x + 2x2 Solving for variable 'x'. Reorder the terms: 2 + 5 + -37x + -3x + 27x2 + -2x2 = -5 + 3x + 2x2 + 5 + -3x + -2x2 Combine like terms: 2 + 5 = 7 7 + -37x + -3x + 27x2 + -2x2 = -5 + 3x + 2x2 + 5 + -3x + -2x2 Combine like terms: -37x + -3x = -40x 7 + -40x + 27x2 + -2x2 = -5 + 3x + 2x2 + 5 + -3x + -2x2 Combine like terms: 27x2 + -2x2 = 25x2 7 + -40x + 25x2 = -5 + 3x + 2x2 + 5 + -3x + -2x2 Reorder the terms: 7 + -40x + 25x2 = -5 + 5 + 3x + -3x + 2x2 + -2x2 Combine like terms: -5 + 5 = 0 7 + -40x + 25x2 = 0 + 3x + -3x + 2x2 + -2x2 7 + -40x + 25x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 7 + -40x + 25x2 = 0 + 2x2 + -2x2 7 + -40x + 25x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 7 + -40x + 25x2 = 0 Factor a trinomial. (1 + -5x)(7 + -5x) = 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 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 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 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4Solution
x = {0.2, 1.4}
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