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Simplifying 176 = (q + 5) * q Reorder the terms: 176 = (5 + q) * q Reorder the terms for easier multiplication: 176 = q(5 + q) 176 = (5 * q + q * q) 176 = (5q + q2) Solving 176 = 5q + q2 Solving for variable 'q'. Reorder the terms: 176 + -5q + -1q2 = 5q + -5q + q2 + -1q2 Combine like terms: 5q + -5q = 0 176 + -5q + -1q2 = 0 + q2 + -1q2 176 + -5q + -1q2 = q2 + -1q2 Combine like terms: q2 + -1q2 = 0 176 + -5q + -1q2 = 0 Factor a trinomial. (11 + -1q)(16 + q) = 0Subproblem 1
Set the factor '(11 + -1q)' equal to zero and attempt to solve: Simplifying 11 + -1q = 0 Solving 11 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1q = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1q = 0 + -11 -1q = 0 + -11 Combine like terms: 0 + -11 = -11 -1q = -11 Divide each side by '-1'. q = 11 Simplifying q = 11Subproblem 2
Set the factor '(16 + q)' equal to zero and attempt to solve: Simplifying 16 + q = 0 Solving 16 + q = 0 Move all terms containing q to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + q = 0 + -16 Combine like terms: 16 + -16 = 0 0 + q = 0 + -16 q = 0 + -16 Combine like terms: 0 + -16 = -16 q = -16 Simplifying q = -16Solution
q = {11, -16}
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