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Simplifying 2x2 + 22x + 312 = 1452 Reorder the terms: 312 + 22x + 2x2 = 1452 Solving 312 + 22x + 2x2 = 1452 Solving for variable 'x'. Reorder the terms: 312 + -1452 + 22x + 2x2 = 1452 + -1452 Combine like terms: 312 + -1452 = -1140 -1140 + 22x + 2x2 = 1452 + -1452 Combine like terms: 1452 + -1452 = 0 -1140 + 22x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-570 + 11x + x2) = 0 Factor a trinomial. 2((-30 + -1x)(19 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + -1x)' equal to zero and attempt to solve: Simplifying -30 + -1x = 0 Solving -30 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + -1x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -1x = 0 + 30 -1x = 0 + 30 Combine like terms: 0 + 30 = 30 -1x = 30 Divide each side by '-1'. x = -30 Simplifying x = -30Subproblem 2
Set the factor '(19 + -1x)' equal to zero and attempt to solve: Simplifying 19 + -1x = 0 Solving 19 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -1x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -1x = 0 + -19 -1x = 0 + -19 Combine like terms: 0 + -19 = -19 -1x = -19 Divide each side by '-1'. x = 19 Simplifying x = 19Solution
x = {-30, 19}
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