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Simplifying Q2 + -2Q + 3 = 38 Reorder the terms: 3 + -2Q + Q2 = 38 Solving 3 + -2Q + Q2 = 38 Solving for variable 'Q'. Reorder the terms: 3 + -38 + -2Q + Q2 = 38 + -38 Combine like terms: 3 + -38 = -35 -35 + -2Q + Q2 = 38 + -38 Combine like terms: 38 + -38 = 0 -35 + -2Q + Q2 = 0 Factor a trinomial. (-5 + -1Q)(7 + -1Q) = 0Subproblem 1
Set the factor '(-5 + -1Q)' equal to zero and attempt to solve: Simplifying -5 + -1Q = 0 Solving -5 + -1Q = 0 Move all terms containing Q to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1Q = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1Q = 0 + 5 -1Q = 0 + 5 Combine like terms: 0 + 5 = 5 -1Q = 5 Divide each side by '-1'. Q = -5 Simplifying Q = -5Subproblem 2
Set the factor '(7 + -1Q)' equal to zero and attempt to solve: Simplifying 7 + -1Q = 0 Solving 7 + -1Q = 0 Move all terms containing Q to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1Q = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1Q = 0 + -7 -1Q = 0 + -7 Combine like terms: 0 + -7 = -7 -1Q = -7 Divide each side by '-1'. Q = 7 Simplifying Q = 7Solution
Q = {-5, 7}
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