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Simplifying -1q2 + -8q + 1 = 0 Reorder the terms: 1 + -8q + -1q2 = 0 Solving 1 + -8q + -1q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 8q + q2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 8q + 1 + q2 = 0 + 1 Reorder the terms: -1 + 1 + 8q + q2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 8q + q2 = 0 + 1 8q + q2 = 0 + 1 Combine like terms: 0 + 1 = 1 8q + q2 = 1 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 = 1 + 16 Reorder the terms: 16 + 8q + q2 = 1 + 16 Combine like terms: 1 + 16 = 17 16 + 8q + q2 = 17 Factor a perfect square on the left side: (q + 4)(q + 4) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (q + 4) equal to 4.123105626 and -4.123105626.Subproblem 1
q + 4 = 4.123105626 Simplifying q + 4 = 4.123105626 Reorder the terms: 4 + q = 4.123105626 Solving 4 + q = 4.123105626 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 = 4.123105626 + -4 Combine like terms: 4 + -4 = 0 0 + q = 4.123105626 + -4 q = 4.123105626 + -4 Combine like terms: 4.123105626 + -4 = 0.123105626 q = 0.123105626 Simplifying q = 0.123105626Subproblem 2
q + 4 = -4.123105626 Simplifying q + 4 = -4.123105626 Reorder the terms: 4 + q = -4.123105626 Solving 4 + q = -4.123105626 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 = -4.123105626 + -4 Combine like terms: 4 + -4 = 0 0 + q = -4.123105626 + -4 q = -4.123105626 + -4 Combine like terms: -4.123105626 + -4 = -8.123105626 q = -8.123105626 Simplifying q = -8.123105626Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.123105626, -8.123105626}
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