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Simplifying 2q2 + 60q = -34 Reorder the terms: 60q + 2q2 = -34 Solving 60q + 2q2 = -34 Solving for variable 'q'. Reorder the terms: 34 + 60q + 2q2 = -34 + 34 Combine like terms: -34 + 34 = 0 34 + 60q + 2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(17 + 30q + q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + 30q + q2)' equal to zero and attempt to solve: Simplifying 17 + 30q + q2 = 0 Solving 17 + 30q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 30q + -17 + q2 = 0 + -17 Reorder the terms: 17 + -17 + 30q + q2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 30q + q2 = 0 + -17 30q + q2 = 0 + -17 Combine like terms: 0 + -17 = -17 30q + q2 = -17 The q term is 30q. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30q + 225 + q2 = -17 + 225 Reorder the terms: 225 + 30q + q2 = -17 + 225 Combine like terms: -17 + 225 = 208 225 + 30q + q2 = 208 Factor a perfect square on the left side: (q + 15)(q + 15) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (q + 15) equal to 14.422205102 and -14.422205102.Subproblem 1
q + 15 = 14.422205102 Simplifying q + 15 = 14.422205102 Reorder the terms: 15 + q = 14.422205102 Solving 15 + q = 14.422205102 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + q = 14.422205102 + -15 Combine like terms: 15 + -15 = 0 0 + q = 14.422205102 + -15 q = 14.422205102 + -15 Combine like terms: 14.422205102 + -15 = -0.577794898 q = -0.577794898 Simplifying q = -0.577794898Subproblem 2
q + 15 = -14.422205102 Simplifying q + 15 = -14.422205102 Reorder the terms: 15 + q = -14.422205102 Solving 15 + q = -14.422205102 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + q = -14.422205102 + -15 Combine like terms: 15 + -15 = 0 0 + q = -14.422205102 + -15 q = -14.422205102 + -15 Combine like terms: -14.422205102 + -15 = -29.422205102 q = -29.422205102 Simplifying q = -29.422205102Solution
The solution to the problem is based on the solutions from the subproblems. q = {-0.577794898, -29.422205102}Solution
q = {-0.577794898, -29.422205102}
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