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Simplifying q2 + -8q = 7 Reorder the terms: -8q + q2 = 7 Solving -8q + q2 = 7 Solving for variable 'q'. Reorder the terms: -7 + -8q + q2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -8q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -8q + 7 + q2 = 0 + 7 Reorder the terms: -7 + 7 + -8q + q2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8q + q2 = 0 + 7 -8q + q2 = 0 + 7 Combine like terms: 0 + 7 = 7 -8q + q2 = 7 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 = 7 + 16 Reorder the terms: 16 + -8q + q2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + -8q + q2 = 23 Factor a perfect square on the left side: (q + -4)(q + -4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (q + -4) equal to 4.795831523 and -4.795831523.Subproblem 1
q + -4 = 4.795831523 Simplifying q + -4 = 4.795831523 Reorder the terms: -4 + q = 4.795831523 Solving -4 + q = 4.795831523 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 = 4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + q = 4.795831523 + 4 q = 4.795831523 + 4 Combine like terms: 4.795831523 + 4 = 8.795831523 q = 8.795831523 Simplifying q = 8.795831523Subproblem 2
q + -4 = -4.795831523 Simplifying q + -4 = -4.795831523 Reorder the terms: -4 + q = -4.795831523 Solving -4 + q = -4.795831523 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 = -4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + q = -4.795831523 + 4 q = -4.795831523 + 4 Combine like terms: -4.795831523 + 4 = -0.795831523 q = -0.795831523 Simplifying q = -0.795831523Solution
The solution to the problem is based on the solutions from the subproblems. q = {8.795831523, -0.795831523}
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