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Simplifying 4(q2 + -6q + 9) = 5(11 + -5q) + -1(q2 + 1) Reorder the terms: 4(9 + -6q + q2) = 5(11 + -5q) + -1(q2 + 1) (9 * 4 + -6q * 4 + q2 * 4) = 5(11 + -5q) + -1(q2 + 1) (36 + -24q + 4q2) = 5(11 + -5q) + -1(q2 + 1) 36 + -24q + 4q2 = (11 * 5 + -5q * 5) + -1(q2 + 1) 36 + -24q + 4q2 = (55 + -25q) + -1(q2 + 1) Reorder the terms: 36 + -24q + 4q2 = 55 + -25q + -1(1 + q2) 36 + -24q + 4q2 = 55 + -25q + (1 * -1 + q2 * -1) 36 + -24q + 4q2 = 55 + -25q + (-1 + -1q2) Reorder the terms: 36 + -24q + 4q2 = 55 + -1 + -25q + -1q2 Combine like terms: 55 + -1 = 54 36 + -24q + 4q2 = 54 + -25q + -1q2 Solving 36 + -24q + 4q2 = 54 + -25q + -1q2 Solving for variable 'q'. Reorder the terms: 36 + -54 + -24q + 25q + 4q2 + q2 = 54 + -25q + -1q2 + -54 + 25q + q2 Combine like terms: 36 + -54 = -18 -18 + -24q + 25q + 4q2 + q2 = 54 + -25q + -1q2 + -54 + 25q + q2 Combine like terms: -24q + 25q = 1q -18 + 1q + 4q2 + q2 = 54 + -25q + -1q2 + -54 + 25q + q2 Combine like terms: 4q2 + q2 = 5q2 -18 + 1q + 5q2 = 54 + -25q + -1q2 + -54 + 25q + q2 Reorder the terms: -18 + 1q + 5q2 = 54 + -54 + -25q + 25q + -1q2 + q2 Combine like terms: 54 + -54 = 0 -18 + 1q + 5q2 = 0 + -25q + 25q + -1q2 + q2 -18 + 1q + 5q2 = -25q + 25q + -1q2 + q2 Combine like terms: -25q + 25q = 0 -18 + 1q + 5q2 = 0 + -1q2 + q2 -18 + 1q + 5q2 = -1q2 + q2 Combine like terms: -1q2 + q2 = 0 -18 + 1q + 5q2 = 0 Factor a trinomial. (-2 + -1q)(9 + -5q) = 0Subproblem 1
Set the factor '(-2 + -1q)' equal to zero and attempt to solve: Simplifying -2 + -1q = 0 Solving -2 + -1q = 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 + -1q = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1q = 0 + 2 -1q = 0 + 2 Combine like terms: 0 + 2 = 2 -1q = 2 Divide each side by '-1'. q = -2 Simplifying q = -2Subproblem 2
Set the factor '(9 + -5q)' equal to zero and attempt to solve: Simplifying 9 + -5q = 0 Solving 9 + -5q = 0 Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5q = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5q = 0 + -9 -5q = 0 + -9 Combine like terms: 0 + -9 = -9 -5q = -9 Divide each side by '-5'. q = 1.8 Simplifying q = 1.8Solution
q = {-2, 1.8}
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