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Simplifying 2q2 = 14 + -1q Solving 2q2 = 14 + -1q Solving for variable 'q'. Reorder the terms: -14 + q + 2q2 = 14 + -1q + -14 + q Reorder the terms: -14 + q + 2q2 = 14 + -14 + -1q + q Combine like terms: 14 + -14 = 0 -14 + q + 2q2 = 0 + -1q + q -14 + q + 2q2 = -1q + q Combine like terms: -1q + q = 0 -14 + q + 2q2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7 + 0.5q + q2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 0.5q + 7 + q2 = 0 + 7 Reorder the terms: -7 + 7 + 0.5q + q2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 0.5q + q2 = 0 + 7 0.5q + q2 = 0 + 7 Combine like terms: 0 + 7 = 7 0.5q + q2 = 7 The q term is q. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5q + 0.25 + q2 = 7 + 0.25 Reorder the terms: 0.25 + 0.5q + q2 = 7 + 0.25 Combine like terms: 7 + 0.25 = 7.25 0.25 + 0.5q + q2 = 7.25 Factor a perfect square on the left side: (q + 0.5)(q + 0.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (q + 0.5) equal to 2.692582404 and -2.692582404.Subproblem 1
q + 0.5 = 2.692582404 Simplifying q + 0.5 = 2.692582404 Reorder the terms: 0.5 + q = 2.692582404 Solving 0.5 + q = 2.692582404 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q = 2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = 2.692582404 + -0.5 q = 2.692582404 + -0.5 Combine like terms: 2.692582404 + -0.5 = 2.192582404 q = 2.192582404 Simplifying q = 2.192582404Subproblem 2
q + 0.5 = -2.692582404 Simplifying q + 0.5 = -2.692582404 Reorder the terms: 0.5 + q = -2.692582404 Solving 0.5 + q = -2.692582404 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q = -2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = -2.692582404 + -0.5 q = -2.692582404 + -0.5 Combine like terms: -2.692582404 + -0.5 = -3.192582404 q = -3.192582404 Simplifying q = -3.192582404Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.192582404, -3.192582404}
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