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Simplifying -176Q + -128 = -24Q2 Reorder the terms: -128 + -176Q = -24Q2 Solving -128 + -176Q = -24Q2 Solving for variable 'Q'. Combine like terms: -24Q2 + 24Q2 = 0 -128 + -176Q + 24Q2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-16 + -22Q + 3Q2) = 0 Factor a trinomial. 8((-2 + -3Q)(8 + -1Q)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-2 + -3Q)' equal to zero and attempt to solve: Simplifying -2 + -3Q = 0 Solving -2 + -3Q = 0 Move all terms containing Q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3Q = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3Q = 0 + 2 -3Q = 0 + 2 Combine like terms: 0 + 2 = 2 -3Q = 2 Divide each side by '-3'. Q = -0.6666666667 Simplifying Q = -0.6666666667Subproblem 2
Set the factor '(8 + -1Q)' equal to zero and attempt to solve: Simplifying 8 + -1Q = 0 Solving 8 + -1Q = 0 Move all terms containing Q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1Q = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1Q = 0 + -8 -1Q = 0 + -8 Combine like terms: 0 + -8 = -8 -1Q = -8 Divide each side by '-1'. Q = 8 Simplifying Q = 8Solution
Q = {-0.6666666667, 8}
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