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Simplifying 28 + 6q + -1q2 = 0 Solving 28 + 6q + -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'. -28 + -6q + q2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -6q + 28 + q2 = 0 + 28 Reorder the terms: -28 + 28 + -6q + q2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -6q + q2 = 0 + 28 -6q + q2 = 0 + 28 Combine like terms: 0 + 28 = 28 -6q + q2 = 28 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 = 28 + 9 Reorder the terms: 9 + -6q + q2 = 28 + 9 Combine like terms: 28 + 9 = 37 9 + -6q + q2 = 37 Factor a perfect square on the left side: (q + -3)(q + -3) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (q + -3) equal to 6.08276253 and -6.08276253.Subproblem 1
q + -3 = 6.08276253 Simplifying q + -3 = 6.08276253 Reorder the terms: -3 + q = 6.08276253 Solving -3 + q = 6.08276253 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 = 6.08276253 + 3 Combine like terms: -3 + 3 = 0 0 + q = 6.08276253 + 3 q = 6.08276253 + 3 Combine like terms: 6.08276253 + 3 = 9.08276253 q = 9.08276253 Simplifying q = 9.08276253Subproblem 2
q + -3 = -6.08276253 Simplifying q + -3 = -6.08276253 Reorder the terms: -3 + q = -6.08276253 Solving -3 + q = -6.08276253 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 = -6.08276253 + 3 Combine like terms: -3 + 3 = 0 0 + q = -6.08276253 + 3 q = -6.08276253 + 3 Combine like terms: -6.08276253 + 3 = -3.08276253 q = -3.08276253 Simplifying q = -3.08276253Solution
The solution to the problem is based on the solutions from the subproblems. q = {9.08276253, -3.08276253}
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