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Simplifying q2 + 12q + 25 = 0 Reorder the terms: 25 + 12q + q2 = 0 Solving 25 + 12q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 12q + -25 + q2 = 0 + -25 Reorder the terms: 25 + -25 + 12q + q2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 12q + q2 = 0 + -25 12q + q2 = 0 + -25 Combine like terms: 0 + -25 = -25 12q + q2 = -25 The q term is 12q. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12q + 36 + q2 = -25 + 36 Reorder the terms: 36 + 12q + q2 = -25 + 36 Combine like terms: -25 + 36 = 11 36 + 12q + q2 = 11 Factor a perfect square on the left side: (q + 6)(q + 6) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (q + 6) equal to 3.31662479 and -3.31662479.Subproblem 1
q + 6 = 3.31662479 Simplifying q + 6 = 3.31662479 Reorder the terms: 6 + q = 3.31662479 Solving 6 + q = 3.31662479 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + q = 3.31662479 + -6 Combine like terms: 6 + -6 = 0 0 + q = 3.31662479 + -6 q = 3.31662479 + -6 Combine like terms: 3.31662479 + -6 = -2.68337521 q = -2.68337521 Simplifying q = -2.68337521Subproblem 2
q + 6 = -3.31662479 Simplifying q + 6 = -3.31662479 Reorder the terms: 6 + q = -3.31662479 Solving 6 + q = -3.31662479 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + q = -3.31662479 + -6 Combine like terms: 6 + -6 = 0 0 + q = -3.31662479 + -6 q = -3.31662479 + -6 Combine like terms: -3.31662479 + -6 = -9.31662479 q = -9.31662479 Simplifying q = -9.31662479Solution
The solution to the problem is based on the solutions from the subproblems. q = {-2.68337521, -9.31662479}
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