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Simplifying 4q2 + -5q = 3q2 + -8q + 28 Reorder the terms: -5q + 4q2 = 3q2 + -8q + 28 Reorder the terms: -5q + 4q2 = 28 + -8q + 3q2 Solving -5q + 4q2 = 28 + -8q + 3q2 Solving for variable 'q'. Reorder the terms: -28 + -5q + 8q + 4q2 + -3q2 = 28 + -8q + 3q2 + -28 + 8q + -3q2 Combine like terms: -5q + 8q = 3q -28 + 3q + 4q2 + -3q2 = 28 + -8q + 3q2 + -28 + 8q + -3q2 Combine like terms: 4q2 + -3q2 = 1q2 -28 + 3q + 1q2 = 28 + -8q + 3q2 + -28 + 8q + -3q2 Reorder the terms: -28 + 3q + 1q2 = 28 + -28 + -8q + 8q + 3q2 + -3q2 Combine like terms: 28 + -28 = 0 -28 + 3q + 1q2 = 0 + -8q + 8q + 3q2 + -3q2 -28 + 3q + 1q2 = -8q + 8q + 3q2 + -3q2 Combine like terms: -8q + 8q = 0 -28 + 3q + 1q2 = 0 + 3q2 + -3q2 -28 + 3q + 1q2 = 3q2 + -3q2 Combine like terms: 3q2 + -3q2 = 0 -28 + 3q + 1q2 = 0 Factor a trinomial. (-7 + -1q)(4 + -1q) = 0Subproblem 1
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 = -7Subproblem 2
Set the factor '(4 + -1q)' equal to zero and attempt to solve: Simplifying 4 + -1q = 0 Solving 4 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1q = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1q = 0 + -4 -1q = 0 + -4 Combine like terms: 0 + -4 = -4 -1q = -4 Divide each side by '-1'. q = 4 Simplifying q = 4Solution
q = {-7, 4}
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