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Simplifying q2 + 6q = -7 Reorder the terms: 6q + q2 = -7 Solving 6q + q2 = -7 Solving for variable 'q'. Reorder the terms: 7 + 6q + q2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 6q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6q + -7 + q2 = 0 + -7 Reorder the terms: 7 + -7 + 6q + q2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6q + q2 = 0 + -7 6q + q2 = 0 + -7 Combine like terms: 0 + -7 = -7 6q + q2 = -7 The q term is 6q. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6q + 9 + q2 = -7 + 9 Reorder the terms: 9 + 6q + q2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + 6q + q2 = 2 Factor a perfect square on the left side: (q + 3)(q + 3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (q + 3) equal to 1.414213562 and -1.414213562.Subproblem 1
q + 3 = 1.414213562 Simplifying q + 3 = 1.414213562 Reorder the terms: 3 + q = 1.414213562 Solving 3 + q = 1.414213562 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + q = 1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + q = 1.414213562 + -3 q = 1.414213562 + -3 Combine like terms: 1.414213562 + -3 = -1.585786438 q = -1.585786438 Simplifying q = -1.585786438Subproblem 2
q + 3 = -1.414213562 Simplifying q + 3 = -1.414213562 Reorder the terms: 3 + q = -1.414213562 Solving 3 + q = -1.414213562 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + q = -1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + q = -1.414213562 + -3 q = -1.414213562 + -3 Combine like terms: -1.414213562 + -3 = -4.414213562 q = -4.414213562 Simplifying q = -4.414213562Solution
The solution to the problem is based on the solutions from the subproblems. q = {-1.585786438, -4.414213562}
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