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Simplifying q2 + 8q = 27 Reorder the terms: 8q + q2 = 27 Solving 8q + q2 = 27 Solving for variable 'q'. Reorder the terms: -27 + 8q + q2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 8q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 8q + 27 + q2 = 0 + 27 Reorder the terms: -27 + 27 + 8q + q2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 8q + q2 = 0 + 27 8q + q2 = 0 + 27 Combine like terms: 0 + 27 = 27 8q + q2 = 27 The q term is 8q. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8q + 16 + q2 = 27 + 16 Reorder the terms: 16 + 8q + q2 = 27 + 16 Combine like terms: 27 + 16 = 43 16 + 8q + q2 = 43 Factor a perfect square on the left side: (q + 4)(q + 4) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (q + 4) equal to 6.557438524 and -6.557438524.Subproblem 1
q + 4 = 6.557438524 Simplifying q + 4 = 6.557438524 Reorder the terms: 4 + q = 6.557438524 Solving 4 + q = 6.557438524 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + q = 6.557438524 + -4 Combine like terms: 4 + -4 = 0 0 + q = 6.557438524 + -4 q = 6.557438524 + -4 Combine like terms: 6.557438524 + -4 = 2.557438524 q = 2.557438524 Simplifying q = 2.557438524Subproblem 2
q + 4 = -6.557438524 Simplifying q + 4 = -6.557438524 Reorder the terms: 4 + q = -6.557438524 Solving 4 + q = -6.557438524 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + q = -6.557438524 + -4 Combine like terms: 4 + -4 = 0 0 + q = -6.557438524 + -4 q = -6.557438524 + -4 Combine like terms: -6.557438524 + -4 = -10.557438524 q = -10.557438524 Simplifying q = -10.557438524Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.557438524, -10.557438524}
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