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Simplifying 31x2 + -55x + 18 = 6x2 + -6 Reorder the terms: 18 + -55x + 31x2 = 6x2 + -6 Reorder the terms: 18 + -55x + 31x2 = -6 + 6x2 Solving 18 + -55x + 31x2 = -6 + 6x2 Solving for variable 'x'. Reorder the terms: 18 + 6 + -55x + 31x2 + -6x2 = -6 + 6x2 + 6 + -6x2 Combine like terms: 18 + 6 = 24 24 + -55x + 31x2 + -6x2 = -6 + 6x2 + 6 + -6x2 Combine like terms: 31x2 + -6x2 = 25x2 24 + -55x + 25x2 = -6 + 6x2 + 6 + -6x2 Reorder the terms: 24 + -55x + 25x2 = -6 + 6 + 6x2 + -6x2 Combine like terms: -6 + 6 = 0 24 + -55x + 25x2 = 0 + 6x2 + -6x2 24 + -55x + 25x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 24 + -55x + 25x2 = 0 Factor a trinomial. (3 + -5x)(8 + -5x) = 0Subproblem 1
Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve: Simplifying 8 + -5x = 0 Solving 8 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x = 0 + -8 -5x = 0 + -8 Combine like terms: 0 + -8 = -8 -5x = -8 Divide each side by '-5'. x = 1.6 Simplifying x = 1.6Solution
x = {0.6, 1.6}
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