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Simplifying 2q2 + 32q = 66 Reorder the terms: 32q + 2q2 = 66 Solving 32q + 2q2 = 66 Solving for variable 'q'. Reorder the terms: -66 + 32q + 2q2 = 66 + -66 Combine like terms: 66 + -66 = 0 -66 + 32q + 2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + 16q + q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-33 + 16q + q2)' equal to zero and attempt to solve: Simplifying -33 + 16q + q2 = 0 Solving -33 + 16q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 16q + 33 + q2 = 0 + 33 Reorder the terms: -33 + 33 + 16q + q2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 16q + q2 = 0 + 33 16q + q2 = 0 + 33 Combine like terms: 0 + 33 = 33 16q + q2 = 33 The q term is 16q. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16q + 64 + q2 = 33 + 64 Reorder the terms: 64 + 16q + q2 = 33 + 64 Combine like terms: 33 + 64 = 97 64 + 16q + q2 = 97 Factor a perfect square on the left side: (q + 8)(q + 8) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (q + 8) equal to 9.848857802 and -9.848857802.Subproblem 1
q + 8 = 9.848857802 Simplifying q + 8 = 9.848857802 Reorder the terms: 8 + q = 9.848857802 Solving 8 + q = 9.848857802 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + q = 9.848857802 + -8 Combine like terms: 8 + -8 = 0 0 + q = 9.848857802 + -8 q = 9.848857802 + -8 Combine like terms: 9.848857802 + -8 = 1.848857802 q = 1.848857802 Simplifying q = 1.848857802Subproblem 2
q + 8 = -9.848857802 Simplifying q + 8 = -9.848857802 Reorder the terms: 8 + q = -9.848857802 Solving 8 + q = -9.848857802 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + q = -9.848857802 + -8 Combine like terms: 8 + -8 = 0 0 + q = -9.848857802 + -8 q = -9.848857802 + -8 Combine like terms: -9.848857802 + -8 = -17.848857802 q = -17.848857802 Simplifying q = -17.848857802Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.848857802, -17.848857802}Solution
q = {1.848857802, -17.848857802}
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