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Simplifying 4x2 + -31x + 45 = -7 + 10 Reorder the terms: 45 + -31x + 4x2 = -7 + 10 Combine like terms: -7 + 10 = 3 45 + -31x + 4x2 = 3 Solving 45 + -31x + 4x2 = 3 Solving for variable 'x'. Reorder the terms: 45 + -3 + -31x + 4x2 = 3 + -3 Combine like terms: 45 + -3 = 42 42 + -31x + 4x2 = 3 + -3 Combine like terms: 3 + -3 = 0 42 + -31x + 4x2 = 0 Factor a trinomial. (7 + -4x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {1.75, 6}
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