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Simplifying 3x + 1 + x2 + 2 = 31 Reorder the terms: 1 + 2 + 3x + x2 = 31 Combine like terms: 1 + 2 = 3 3 + 3x + x2 = 31 Solving 3 + 3x + x2 = 31 Solving for variable 'x'. Reorder the terms: 3 + -31 + 3x + x2 = 31 + -31 Combine like terms: 3 + -31 = -28 -28 + 3x + x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -28 + 3x + x2 = 0 Factor a trinomial. (-7 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-7, 4}
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