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Simplifying 1034 = x2 + 30x + -110 Reorder the terms: 1034 = -110 + 30x + x2 Solving 1034 = -110 + 30x + x2 Solving for variable 'x'. Combine like terms: 1034 + 110 = 1144 1144 + -30x + -1x2 = -110 + 30x + x2 + 110 + -30x + -1x2 Reorder the terms: 1144 + -30x + -1x2 = -110 + 110 + 30x + -30x + x2 + -1x2 Combine like terms: -110 + 110 = 0 1144 + -30x + -1x2 = 0 + 30x + -30x + x2 + -1x2 1144 + -30x + -1x2 = 30x + -30x + x2 + -1x2 Combine like terms: 30x + -30x = 0 1144 + -30x + -1x2 = 0 + x2 + -1x2 1144 + -30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1144 + -30x + -1x2 = 0 Factor a trinomial. (22 + -1x)(52 + x) = 0Subproblem 1
Set the factor '(22 + -1x)' equal to zero and attempt to solve: Simplifying 22 + -1x = 0 Solving 22 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + -1x = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -1x = 0 + -22 -1x = 0 + -22 Combine like terms: 0 + -22 = -22 -1x = -22 Divide each side by '-1'. x = 22 Simplifying x = 22Subproblem 2
Set the factor '(52 + x)' equal to zero and attempt to solve: Simplifying 52 + x = 0 Solving 52 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-52' to each side of the equation. 52 + -52 + x = 0 + -52 Combine like terms: 52 + -52 = 0 0 + x = 0 + -52 x = 0 + -52 Combine like terms: 0 + -52 = -52 x = -52 Simplifying x = -52Solution
x = {22, -52}
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