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Simplifying (20 + -1q)(20 + -1q) = q + 22 Multiply (20 + -1q) * (20 + -1q) (20(20 + -1q) + -1q * (20 + -1q)) = q + 22 ((20 * 20 + -1q * 20) + -1q * (20 + -1q)) = q + 22 ((400 + -20q) + -1q * (20 + -1q)) = q + 22 (400 + -20q + (20 * -1q + -1q * -1q)) = q + 22 (400 + -20q + (-20q + 1q2)) = q + 22 Combine like terms: -20q + -20q = -40q (400 + -40q + 1q2) = q + 22 Reorder the terms: 400 + -40q + 1q2 = 22 + q Solving 400 + -40q + 1q2 = 22 + q Solving for variable 'q'. Reorder the terms: 400 + -22 + -40q + -1q + 1q2 = 22 + q + -22 + -1q Combine like terms: 400 + -22 = 378 378 + -40q + -1q + 1q2 = 22 + q + -22 + -1q Combine like terms: -40q + -1q = -41q 378 + -41q + 1q2 = 22 + q + -22 + -1q Reorder the terms: 378 + -41q + 1q2 = 22 + -22 + q + -1q Combine like terms: 22 + -22 = 0 378 + -41q + 1q2 = 0 + q + -1q 378 + -41q + 1q2 = q + -1q Combine like terms: q + -1q = 0 378 + -41q + 1q2 = 0 Factor a trinomial. (14 + -1q)(27 + -1q) = 0Subproblem 1
Set the factor '(14 + -1q)' equal to zero and attempt to solve: Simplifying 14 + -1q = 0 Solving 14 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1q = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1q = 0 + -14 -1q = 0 + -14 Combine like terms: 0 + -14 = -14 -1q = -14 Divide each side by '-1'. q = 14 Simplifying q = 14Subproblem 2
Set the factor '(27 + -1q)' equal to zero and attempt to solve: Simplifying 27 + -1q = 0 Solving 27 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -1q = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1q = 0 + -27 -1q = 0 + -27 Combine like terms: 0 + -27 = -27 -1q = -27 Divide each side by '-1'. q = 27 Simplifying q = 27Solution
q = {14, 27}
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