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Simplifying q2 + 12q = 29 Reorder the terms: 12q + q2 = 29 Solving 12q + q2 = 29 Solving for variable 'q'. Reorder the terms: -29 + 12q + q2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 12q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 12q + 29 + q2 = 0 + 29 Reorder the terms: -29 + 29 + 12q + q2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 12q + q2 = 0 + 29 12q + q2 = 0 + 29 Combine like terms: 0 + 29 = 29 12q + q2 = 29 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 = 29 + 36 Reorder the terms: 36 + 12q + q2 = 29 + 36 Combine like terms: 29 + 36 = 65 36 + 12q + q2 = 65 Factor a perfect square on the left side: (q + 6)(q + 6) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (q + 6) equal to 8.062257748 and -8.062257748.Subproblem 1
q + 6 = 8.062257748 Simplifying q + 6 = 8.062257748 Reorder the terms: 6 + q = 8.062257748 Solving 6 + q = 8.062257748 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 = 8.062257748 + -6 Combine like terms: 6 + -6 = 0 0 + q = 8.062257748 + -6 q = 8.062257748 + -6 Combine like terms: 8.062257748 + -6 = 2.062257748 q = 2.062257748 Simplifying q = 2.062257748Subproblem 2
q + 6 = -8.062257748 Simplifying q + 6 = -8.062257748 Reorder the terms: 6 + q = -8.062257748 Solving 6 + q = -8.062257748 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 = -8.062257748 + -6 Combine like terms: 6 + -6 = 0 0 + q = -8.062257748 + -6 q = -8.062257748 + -6 Combine like terms: -8.062257748 + -6 = -14.062257748 q = -14.062257748 Simplifying q = -14.062257748Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.062257748, -14.062257748}
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