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Simplifying 4q2 + -48q + 68 = 0 Reorder the terms: 68 + -48q + 4q2 = 0 Solving 68 + -48q + 4q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '4'. 4(17 + -12q + q2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(17 + -12q + q2)' equal to zero and attempt to solve: Simplifying 17 + -12q + q2 = 0 Solving 17 + -12q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -12q + -17 + q2 = 0 + -17 Reorder the terms: 17 + -17 + -12q + q2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -12q + q2 = 0 + -17 -12q + q2 = 0 + -17 Combine like terms: 0 + -17 = -17 -12q + q2 = -17 The q term is -12q. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12q + 36 + q2 = -17 + 36 Reorder the terms: 36 + -12q + q2 = -17 + 36 Combine like terms: -17 + 36 = 19 36 + -12q + q2 = 19 Factor a perfect square on the left side: (q + -6)(q + -6) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (q + -6) equal to 4.358898944 and -4.358898944.Subproblem 1
q + -6 = 4.358898944 Simplifying q + -6 = 4.358898944 Reorder the terms: -6 + q = 4.358898944 Solving -6 + q = 4.358898944 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + q = 4.358898944 + 6 Combine like terms: -6 + 6 = 0 0 + q = 4.358898944 + 6 q = 4.358898944 + 6 Combine like terms: 4.358898944 + 6 = 10.358898944 q = 10.358898944 Simplifying q = 10.358898944Subproblem 2
q + -6 = -4.358898944 Simplifying q + -6 = -4.358898944 Reorder the terms: -6 + q = -4.358898944 Solving -6 + q = -4.358898944 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + q = -4.358898944 + 6 Combine like terms: -6 + 6 = 0 0 + q = -4.358898944 + 6 q = -4.358898944 + 6 Combine like terms: -4.358898944 + 6 = 1.641101056 q = 1.641101056 Simplifying q = 1.641101056Solution
The solution to the problem is based on the solutions from the subproblems. q = {10.358898944, 1.641101056}Solution
q = {10.358898944, 1.641101056}
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