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Simplifying 2q2 + 45q = 23 Reorder the terms: 45q + 2q2 = 23 Solving 45q + 2q2 = 23 Solving for variable 'q'. Reorder the terms: -23 + 45q + 2q2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 45q + 2q2 = 0 Factor a trinomial. (-23 + -1q)(1 + -2q) = 0Subproblem 1
Set the factor '(-23 + -1q)' equal to zero and attempt to solve: Simplifying -23 + -1q = 0 Solving -23 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -1q = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -1q = 0 + 23 -1q = 0 + 23 Combine like terms: 0 + 23 = 23 -1q = 23 Divide each side by '-1'. q = -23 Simplifying q = -23Subproblem 2
Set the factor '(1 + -2q)' equal to zero and attempt to solve: Simplifying 1 + -2q = 0 Solving 1 + -2q = 0 Move all terms containing q to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2q = 0 + -1 -2q = 0 + -1 Combine like terms: 0 + -1 = -1 -2q = -1 Divide each side by '-2'. q = 0.5 Simplifying q = 0.5Solution
q = {-23, 0.5}
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