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Simplifying 0 = 2q2 + -14q + 17 Reorder the terms: 0 = 17 + -14q + 2q2 Solving 0 = 17 + -14q + 2q2 Solving for variable 'q'. Combine like terms: 0 + -17 = -17 -17 + 14q + -2q2 = 17 + -14q + 2q2 + -17 + 14q + -2q2 Reorder the terms: -17 + 14q + -2q2 = 17 + -17 + -14q + 14q + 2q2 + -2q2 Combine like terms: 17 + -17 = 0 -17 + 14q + -2q2 = 0 + -14q + 14q + 2q2 + -2q2 -17 + 14q + -2q2 = -14q + 14q + 2q2 + -2q2 Combine like terms: -14q + 14q = 0 -17 + 14q + -2q2 = 0 + 2q2 + -2q2 -17 + 14q + -2q2 = 2q2 + -2q2 Combine like terms: 2q2 + -2q2 = 0 -17 + 14q + -2q2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 8.5 + -7q + q2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -7q + -8.5 + q2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -7q + q2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -7q + q2 = 0 + -8.5 -7q + q2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -7q + q2 = -8.5 The q term is -7q. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7q + 12.25 + q2 = -8.5 + 12.25 Reorder the terms: 12.25 + -7q + q2 = -8.5 + 12.25 Combine like terms: -8.5 + 12.25 = 3.75 12.25 + -7q + q2 = 3.75 Factor a perfect square on the left side: (q + -3.5)(q + -3.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (q + -3.5) equal to 1.936491673 and -1.936491673.Subproblem 1
q + -3.5 = 1.936491673 Simplifying q + -3.5 = 1.936491673 Reorder the terms: -3.5 + q = 1.936491673 Solving -3.5 + q = 1.936491673 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + q = 1.936491673 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + q = 1.936491673 + 3.5 q = 1.936491673 + 3.5 Combine like terms: 1.936491673 + 3.5 = 5.436491673 q = 5.436491673 Simplifying q = 5.436491673Subproblem 2
q + -3.5 = -1.936491673 Simplifying q + -3.5 = -1.936491673 Reorder the terms: -3.5 + q = -1.936491673 Solving -3.5 + q = -1.936491673 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + q = -1.936491673 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + q = -1.936491673 + 3.5 q = -1.936491673 + 3.5 Combine like terms: -1.936491673 + 3.5 = 1.563508327 q = 1.563508327 Simplifying q = 1.563508327Solution
The solution to the problem is based on the solutions from the subproblems. q = {5.436491673, 1.563508327}
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