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Simplifying 4q + q2 + 4 = 25 Reorder the terms: 4 + 4q + q2 = 25 Solving 4 + 4q + q2 = 25 Solving for variable 'q'. Reorder the terms: 4 + -25 + 4q + q2 = 25 + -25 Combine like terms: 4 + -25 = -21 -21 + 4q + q2 = 25 + -25 Combine like terms: 25 + -25 = 0 -21 + 4q + q2 = 0 Factor a trinomial. (-7 + -1q)(3 + -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 '(3 + -1q)' equal to zero and attempt to solve: Simplifying 3 + -1q = 0 Solving 3 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1q = 0 + -3 -1q = 0 + -3 Combine like terms: 0 + -3 = -3 -1q = -3 Divide each side by '-1'. q = 3 Simplifying q = 3Solution
q = {-7, 3}
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