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Simplifying 4x2 + -31x + 38 = -4x + 3 Reorder the terms: 38 + -31x + 4x2 = -4x + 3 Reorder the terms: 38 + -31x + 4x2 = 3 + -4x Solving 38 + -31x + 4x2 = 3 + -4x Solving for variable 'x'. Reorder the terms: 38 + -3 + -31x + 4x + 4x2 = 3 + -4x + -3 + 4x Combine like terms: 38 + -3 = 35 35 + -31x + 4x + 4x2 = 3 + -4x + -3 + 4x Combine like terms: -31x + 4x = -27x 35 + -27x + 4x2 = 3 + -4x + -3 + 4x Reorder the terms: 35 + -27x + 4x2 = 3 + -3 + -4x + 4x Combine like terms: 3 + -3 = 0 35 + -27x + 4x2 = 0 + -4x + 4x 35 + -27x + 4x2 = -4x + 4x Combine like terms: -4x + 4x = 0 35 + -27x + 4x2 = 0 Factor a trinomial. (7 + -4x)(5 + -1x) = 0Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 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 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {1.75, 5}
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