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Simplifying q2 + 3q + -120 = 0 Reorder the terms: -120 + 3q + q2 = 0 Solving -120 + 3q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 3q + 120 + q2 = 0 + 120 Reorder the terms: -120 + 120 + 3q + q2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 3q + q2 = 0 + 120 3q + q2 = 0 + 120 Combine like terms: 0 + 120 = 120 3q + q2 = 120 The q term is 3q. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3q + 2.25 + q2 = 120 + 2.25 Reorder the terms: 2.25 + 3q + q2 = 120 + 2.25 Combine like terms: 120 + 2.25 = 122.25 2.25 + 3q + q2 = 122.25 Factor a perfect square on the left side: (q + 1.5)(q + 1.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (q + 1.5) equal to 11.056672194 and -11.056672194.Subproblem 1
q + 1.5 = 11.056672194 Simplifying q + 1.5 = 11.056672194 Reorder the terms: 1.5 + q = 11.056672194 Solving 1.5 + q = 11.056672194 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + q = 11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + q = 11.056672194 + -1.5 q = 11.056672194 + -1.5 Combine like terms: 11.056672194 + -1.5 = 9.556672194 q = 9.556672194 Simplifying q = 9.556672194Subproblem 2
q + 1.5 = -11.056672194 Simplifying q + 1.5 = -11.056672194 Reorder the terms: 1.5 + q = -11.056672194 Solving 1.5 + q = -11.056672194 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + q = -11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + q = -11.056672194 + -1.5 q = -11.056672194 + -1.5 Combine like terms: -11.056672194 + -1.5 = -12.556672194 q = -12.556672194 Simplifying q = -12.556672194Solution
The solution to the problem is based on the solutions from the subproblems. q = {9.556672194, -12.556672194}
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