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Simplifying 2q2 + 15q + 3 = 0 Reorder the terms: 3 + 15q + 2q2 = 0 Solving 3 + 15q + 2q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 7.5q + q2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 7.5q + -1.5 + q2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 7.5q + q2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 7.5q + q2 = 0 + -1.5 7.5q + q2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 7.5q + q2 = -1.5 The q term is 7.5q. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5q + 14.0625 + q2 = -1.5 + 14.0625 Reorder the terms: 14.0625 + 7.5q + q2 = -1.5 + 14.0625 Combine like terms: -1.5 + 14.0625 = 12.5625 14.0625 + 7.5q + q2 = 12.5625 Factor a perfect square on the left side: (q + 3.75)(q + 3.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (q + 3.75) equal to 3.54436172 and -3.54436172.Subproblem 1
q + 3.75 = 3.54436172 Simplifying q + 3.75 = 3.54436172 Reorder the terms: 3.75 + q = 3.54436172 Solving 3.75 + q = 3.54436172 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + q = 3.54436172 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + q = 3.54436172 + -3.75 q = 3.54436172 + -3.75 Combine like terms: 3.54436172 + -3.75 = -0.20563828 q = -0.20563828 Simplifying q = -0.20563828Subproblem 2
q + 3.75 = -3.54436172 Simplifying q + 3.75 = -3.54436172 Reorder the terms: 3.75 + q = -3.54436172 Solving 3.75 + q = -3.54436172 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + q = -3.54436172 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + q = -3.54436172 + -3.75 q = -3.54436172 + -3.75 Combine like terms: -3.54436172 + -3.75 = -7.29436172 q = -7.29436172 Simplifying q = -7.29436172Solution
The solution to the problem is based on the solutions from the subproblems. q = {-0.20563828, -7.29436172}
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