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Simplifying 3q2 + -80q + 220 = 0 Reorder the terms: 220 + -80q + 3q2 = 0 Solving 220 + -80q + 3q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 73.33333333 + -26.66666667q + q2 = 0 Move the constant term to the right: Add '-73.33333333' to each side of the equation. 73.33333333 + -26.66666667q + -73.33333333 + q2 = 0 + -73.33333333 Reorder the terms: 73.33333333 + -73.33333333 + -26.66666667q + q2 = 0 + -73.33333333 Combine like terms: 73.33333333 + -73.33333333 = 0.00000000 0.00000000 + -26.66666667q + q2 = 0 + -73.33333333 -26.66666667q + q2 = 0 + -73.33333333 Combine like terms: 0 + -73.33333333 = -73.33333333 -26.66666667q + q2 = -73.33333333 The q term is -26.66666667q. Take half its coefficient (-13.33333334). Square it (177.7777780) and add it to both sides. Add '177.7777780' to each side of the equation. -26.66666667q + 177.7777780 + q2 = -73.33333333 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667q + q2 = -73.33333333 + 177.7777780 Combine like terms: -73.33333333 + 177.7777780 = 104.44444467 177.7777780 + -26.66666667q + q2 = 104.44444467 Factor a perfect square on the left side: (q + -13.33333334)(q + -13.33333334) = 104.44444467 Calculate the square root of the right side: 10.219806489 Break this problem into two subproblems by setting (q + -13.33333334) equal to 10.219806489 and -10.219806489.Subproblem 1
q + -13.33333334 = 10.219806489 Simplifying q + -13.33333334 = 10.219806489 Reorder the terms: -13.33333334 + q = 10.219806489 Solving -13.33333334 + q = 10.219806489 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + q = 10.219806489 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + q = 10.219806489 + 13.33333334 q = 10.219806489 + 13.33333334 Combine like terms: 10.219806489 + 13.33333334 = 23.553139829 q = 23.553139829 Simplifying q = 23.553139829Subproblem 2
q + -13.33333334 = -10.219806489 Simplifying q + -13.33333334 = -10.219806489 Reorder the terms: -13.33333334 + q = -10.219806489 Solving -13.33333334 + q = -10.219806489 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + q = -10.219806489 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + q = -10.219806489 + 13.33333334 q = -10.219806489 + 13.33333334 Combine like terms: -10.219806489 + 13.33333334 = 3.113526851 q = 3.113526851 Simplifying q = 3.113526851Solution
The solution to the problem is based on the solutions from the subproblems. q = {23.553139829, 3.113526851}
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