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Simplifying q2 + -15q + 15 = 0 Reorder the terms: 15 + -15q + q2 = 0 Solving 15 + -15q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -15q + -15 + q2 = 0 + -15 Reorder the terms: 15 + -15 + -15q + q2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -15q + q2 = 0 + -15 -15q + q2 = 0 + -15 Combine like terms: 0 + -15 = -15 -15q + q2 = -15 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 = -15 + 56.25 Reorder the terms: 56.25 + -15q + q2 = -15 + 56.25 Combine like terms: -15 + 56.25 = 41.25 56.25 + -15q + q2 = 41.25 Factor a perfect square on the left side: (q + -7.5)(q + -7.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (q + -7.5) equal to 6.422616289 and -6.422616289.Subproblem 1
q + -7.5 = 6.422616289 Simplifying q + -7.5 = 6.422616289 Reorder the terms: -7.5 + q = 6.422616289 Solving -7.5 + q = 6.422616289 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 = 6.422616289 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + q = 6.422616289 + 7.5 q = 6.422616289 + 7.5 Combine like terms: 6.422616289 + 7.5 = 13.922616289 q = 13.922616289 Simplifying q = 13.922616289Subproblem 2
q + -7.5 = -6.422616289 Simplifying q + -7.5 = -6.422616289 Reorder the terms: -7.5 + q = -6.422616289 Solving -7.5 + q = -6.422616289 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 = -6.422616289 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + q = -6.422616289 + 7.5 q = -6.422616289 + 7.5 Combine like terms: -6.422616289 + 7.5 = 1.077383711 q = 1.077383711 Simplifying q = 1.077383711Solution
The solution to the problem is based on the solutions from the subproblems. q = {13.922616289, 1.077383711}
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