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Simplifying -1q2 + -5q + 120 = 0 Reorder the terms: 120 + -5q + -1q2 = 0 Solving 120 + -5q + -1q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -120 + 5q + q2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 5q + 120 + q2 = 0 + 120 Reorder the terms: -120 + 120 + 5q + q2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 5q + q2 = 0 + 120 5q + q2 = 0 + 120 Combine like terms: 0 + 120 = 120 5q + q2 = 120 The q term is 5q. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5q + 6.25 + q2 = 120 + 6.25 Reorder the terms: 6.25 + 5q + q2 = 120 + 6.25 Combine like terms: 120 + 6.25 = 126.25 6.25 + 5q + q2 = 126.25 Factor a perfect square on the left side: (q + 2.5)(q + 2.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (q + 2.5) equal to 11.236102527 and -11.236102527.Subproblem 1
q + 2.5 = 11.236102527 Simplifying q + 2.5 = 11.236102527 Reorder the terms: 2.5 + q = 11.236102527 Solving 2.5 + q = 11.236102527 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + q = 11.236102527 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + q = 11.236102527 + -2.5 q = 11.236102527 + -2.5 Combine like terms: 11.236102527 + -2.5 = 8.736102527 q = 8.736102527 Simplifying q = 8.736102527Subproblem 2
q + 2.5 = -11.236102527 Simplifying q + 2.5 = -11.236102527 Reorder the terms: 2.5 + q = -11.236102527 Solving 2.5 + q = -11.236102527 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + q = -11.236102527 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + q = -11.236102527 + -2.5 q = -11.236102527 + -2.5 Combine like terms: -11.236102527 + -2.5 = -13.736102527 q = -13.736102527 Simplifying q = -13.736102527Solution
The solution to the problem is based on the solutions from the subproblems. q = {8.736102527, -13.736102527}
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