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Simplifying q2 + 8q = 3 Reorder the terms: 8q + q2 = 3 Solving 8q + q2 = 3 Solving for variable 'q'. Reorder the terms: -3 + 8q + q2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 8q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 8q + 3 + q2 = 0 + 3 Reorder the terms: -3 + 3 + 8q + q2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 8q + q2 = 0 + 3 8q + q2 = 0 + 3 Combine like terms: 0 + 3 = 3 8q + q2 = 3 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 = 3 + 16 Reorder the terms: 16 + 8q + q2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + 8q + q2 = 19 Factor a perfect square on the left side: (q + 4)(q + 4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (q + 4) equal to 4.358898944 and -4.358898944.Subproblem 1
q + 4 = 4.358898944 Simplifying q + 4 = 4.358898944 Reorder the terms: 4 + q = 4.358898944 Solving 4 + q = 4.358898944 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 = 4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + q = 4.358898944 + -4 q = 4.358898944 + -4 Combine like terms: 4.358898944 + -4 = 0.358898944 q = 0.358898944 Simplifying q = 0.358898944Subproblem 2
q + 4 = -4.358898944 Simplifying q + 4 = -4.358898944 Reorder the terms: 4 + q = -4.358898944 Solving 4 + q = -4.358898944 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 = -4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + q = -4.358898944 + -4 q = -4.358898944 + -4 Combine like terms: -4.358898944 + -4 = -8.358898944 q = -8.358898944 Simplifying q = -8.358898944Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.358898944, -8.358898944}
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