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Simplifying -23 = -5q2 + 23q + -49 Reorder the terms: -23 = -49 + 23q + -5q2 Solving -23 = -49 + 23q + -5q2 Solving for variable 'q'. Combine like terms: -23 + 49 = 26 26 + -23q + 5q2 = -49 + 23q + -5q2 + 49 + -23q + 5q2 Reorder the terms: 26 + -23q + 5q2 = -49 + 49 + 23q + -23q + -5q2 + 5q2 Combine like terms: -49 + 49 = 0 26 + -23q + 5q2 = 0 + 23q + -23q + -5q2 + 5q2 26 + -23q + 5q2 = 23q + -23q + -5q2 + 5q2 Combine like terms: 23q + -23q = 0 26 + -23q + 5q2 = 0 + -5q2 + 5q2 26 + -23q + 5q2 = -5q2 + 5q2 Combine like terms: -5q2 + 5q2 = 0 26 + -23q + 5q2 = 0 Factor a trinomial. (2 + -1q)(13 + -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 '(13 + -5q)' equal to zero and attempt to solve: Simplifying 13 + -5q = 0 Solving 13 + -5q = 0 Move all terms containing q to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -5q = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -5q = 0 + -13 -5q = 0 + -13 Combine like terms: 0 + -13 = -13 -5q = -13 Divide each side by '-5'. q = 2.6 Simplifying q = 2.6Solution
q = {2, 2.6}
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