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Simplifying -4q2 + 76q = 68 Reorder the terms: 76q + -4q2 = 68 Solving 76q + -4q2 = 68 Solving for variable 'q'. Reorder the terms: -68 + 76q + -4q2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + 76q + -4q2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-17 + 19q + -1q2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-17 + 19q + -1q2)' equal to zero and attempt to solve: Simplifying -17 + 19q + -1q2 = 0 Solving -17 + 19q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 17 + -19q + q2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + -19q + -17 + q2 = 0 + -17 Reorder the terms: 17 + -17 + -19q + q2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -19q + q2 = 0 + -17 -19q + q2 = 0 + -17 Combine like terms: 0 + -17 = -17 -19q + q2 = -17 The q term is -19q. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19q + 90.25 + q2 = -17 + 90.25 Reorder the terms: 90.25 + -19q + q2 = -17 + 90.25 Combine like terms: -17 + 90.25 = 73.25 90.25 + -19q + q2 = 73.25 Factor a perfect square on the left side: (q + -9.5)(q + -9.5) = 73.25 Calculate the square root of the right side: 8.558621384 Break this problem into two subproblems by setting (q + -9.5) equal to 8.558621384 and -8.558621384.Subproblem 1
q + -9.5 = 8.558621384 Simplifying q + -9.5 = 8.558621384 Reorder the terms: -9.5 + q = 8.558621384 Solving -9.5 + q = 8.558621384 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + q = 8.558621384 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + q = 8.558621384 + 9.5 q = 8.558621384 + 9.5 Combine like terms: 8.558621384 + 9.5 = 18.058621384 q = 18.058621384 Simplifying q = 18.058621384Subproblem 2
q + -9.5 = -8.558621384 Simplifying q + -9.5 = -8.558621384 Reorder the terms: -9.5 + q = -8.558621384 Solving -9.5 + q = -8.558621384 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + q = -8.558621384 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + q = -8.558621384 + 9.5 q = -8.558621384 + 9.5 Combine like terms: -8.558621384 + 9.5 = 0.941378616 q = 0.941378616 Simplifying q = 0.941378616Solution
The solution to the problem is based on the solutions from the subproblems. q = {18.058621384, 0.941378616}Solution
q = {18.058621384, 0.941378616}
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