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Simplifying q2 + -15q = -46 Reorder the terms: -15q + q2 = -46 Solving -15q + q2 = -46 Solving for variable 'q'. Reorder the terms: 46 + -15q + q2 = -46 + 46 Combine like terms: -46 + 46 = 0 46 + -15q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + -15q + -46 + q2 = 0 + -46 Reorder the terms: 46 + -46 + -15q + q2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + -15q + q2 = 0 + -46 -15q + q2 = 0 + -46 Combine like terms: 0 + -46 = -46 -15q + q2 = -46 The q term is -15q. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15q + 56.25 + q2 = -46 + 56.25 Reorder the terms: 56.25 + -15q + q2 = -46 + 56.25 Combine like terms: -46 + 56.25 = 10.25 56.25 + -15q + q2 = 10.25 Factor a perfect square on the left side: (q + -7.5)(q + -7.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (q + -7.5) equal to 3.201562119 and -3.201562119.Subproblem 1
q + -7.5 = 3.201562119 Simplifying q + -7.5 = 3.201562119 Reorder the terms: -7.5 + q = 3.201562119 Solving -7.5 + q = 3.201562119 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + q = 3.201562119 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + q = 3.201562119 + 7.5 q = 3.201562119 + 7.5 Combine like terms: 3.201562119 + 7.5 = 10.701562119 q = 10.701562119 Simplifying q = 10.701562119Subproblem 2
q + -7.5 = -3.201562119 Simplifying q + -7.5 = -3.201562119 Reorder the terms: -7.5 + q = -3.201562119 Solving -7.5 + q = -3.201562119 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + q = -3.201562119 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + q = -3.201562119 + 7.5 q = -3.201562119 + 7.5 Combine like terms: -3.201562119 + 7.5 = 4.298437881 q = 4.298437881 Simplifying q = 4.298437881Solution
The solution to the problem is based on the solutions from the subproblems. q = {10.701562119, 4.298437881}
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