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Simplifying q2 + -100 = 900 + 15q Reorder the terms: -100 + q2 = 900 + 15q Solving -100 + q2 = 900 + 15q Solving for variable 'q'. Reorder the terms: -100 + -900 + -15q + q2 = 900 + 15q + -900 + -15q Combine like terms: -100 + -900 = -1000 -1000 + -15q + q2 = 900 + 15q + -900 + -15q Reorder the terms: -1000 + -15q + q2 = 900 + -900 + 15q + -15q Combine like terms: 900 + -900 = 0 -1000 + -15q + q2 = 0 + 15q + -15q -1000 + -15q + q2 = 15q + -15q Combine like terms: 15q + -15q = 0 -1000 + -15q + q2 = 0 Factor a trinomial. (-25 + -1q)(40 + -1q) = 0Subproblem 1
Set the factor '(-25 + -1q)' equal to zero and attempt to solve: Simplifying -25 + -1q = 0 Solving -25 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -1q = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1q = 0 + 25 -1q = 0 + 25 Combine like terms: 0 + 25 = 25 -1q = 25 Divide each side by '-1'. q = -25 Simplifying q = -25Subproblem 2
Set the factor '(40 + -1q)' equal to zero and attempt to solve: Simplifying 40 + -1q = 0 Solving 40 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1q = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1q = 0 + -40 -1q = 0 + -40 Combine like terms: 0 + -40 = -40 -1q = -40 Divide each side by '-1'. q = 40 Simplifying q = 40Solution
q = {-25, 40}
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