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Simplifying 3q2 + -80q + 240 = 0 Reorder the terms: 240 + -80q + 3q2 = 0 Solving 240 + -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'. 80 + -26.66666667q + q2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -26.66666667q + -80 + q2 = 0 + -80 Reorder the terms: 80 + -80 + -26.66666667q + q2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -26.66666667q + q2 = 0 + -80 -26.66666667q + q2 = 0 + -80 Combine like terms: 0 + -80 = -80 -26.66666667q + q2 = -80 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 = -80 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667q + q2 = -80 + 177.7777780 Combine like terms: -80 + 177.7777780 = 97.777778 177.7777780 + -26.66666667q + q2 = 97.777778 Factor a perfect square on the left side: (q + -13.33333334)(q + -13.33333334) = 97.777778 Calculate the square root of the right side: 9.888264661 Break this problem into two subproblems by setting (q + -13.33333334) equal to 9.888264661 and -9.888264661.Subproblem 1
q + -13.33333334 = 9.888264661 Simplifying q + -13.33333334 = 9.888264661 Reorder the terms: -13.33333334 + q = 9.888264661 Solving -13.33333334 + q = 9.888264661 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 = 9.888264661 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + q = 9.888264661 + 13.33333334 q = 9.888264661 + 13.33333334 Combine like terms: 9.888264661 + 13.33333334 = 23.221598001 q = 23.221598001 Simplifying q = 23.221598001Subproblem 2
q + -13.33333334 = -9.888264661 Simplifying q + -13.33333334 = -9.888264661 Reorder the terms: -13.33333334 + q = -9.888264661 Solving -13.33333334 + q = -9.888264661 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 = -9.888264661 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + q = -9.888264661 + 13.33333334 q = -9.888264661 + 13.33333334 Combine like terms: -9.888264661 + 13.33333334 = 3.445068679 q = 3.445068679 Simplifying q = 3.445068679Solution
The solution to the problem is based on the solutions from the subproblems. q = {23.221598001, 3.445068679}
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