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Simplifying 0.3q2 + q + -40 = 0 Reorder the terms: -40 + q + 0.3q2 = 0 Solving -40 + q + 0.3q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -133.3333333 + 3.333333333q + q2 = 0 Move the constant term to the right: Add '133.3333333' to each side of the equation. -133.3333333 + 3.333333333q + 133.3333333 + q2 = 0 + 133.3333333 Reorder the terms: -133.3333333 + 133.3333333 + 3.333333333q + q2 = 0 + 133.3333333 Combine like terms: -133.3333333 + 133.3333333 = 0.0000000 0.0000000 + 3.333333333q + q2 = 0 + 133.3333333 3.333333333q + q2 = 0 + 133.3333333 Combine like terms: 0 + 133.3333333 = 133.3333333 3.333333333q + q2 = 133.3333333 The q term is q. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 3.333333333q + 0.25 + q2 = 133.3333333 + 0.25 Reorder the terms: 0.25 + 3.333333333q + q2 = 133.3333333 + 0.25 Combine like terms: 133.3333333 + 0.25 = 133.5833333 0.25 + 3.333333333q + q2 = 133.5833333 Factor a perfect square on the left side: (q + 0.5)(q + 0.5) = 133.5833333 Calculate the square root of the right side: 11.55782563 Break this problem into two subproblems by setting (q + 0.5) equal to 11.55782563 and -11.55782563.Subproblem 1
q + 0.5 = 11.55782563 Simplifying q + 0.5 = 11.55782563 Reorder the terms: 0.5 + q = 11.55782563 Solving 0.5 + q = 11.55782563 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q = 11.55782563 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = 11.55782563 + -0.5 q = 11.55782563 + -0.5 Combine like terms: 11.55782563 + -0.5 = 11.05782563 q = 11.05782563 Simplifying q = 11.05782563Subproblem 2
q + 0.5 = -11.55782563 Simplifying q + 0.5 = -11.55782563 Reorder the terms: 0.5 + q = -11.55782563 Solving 0.5 + q = -11.55782563 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + q = -11.55782563 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = -11.55782563 + -0.5 q = -11.55782563 + -0.5 Combine like terms: -11.55782563 + -0.5 = -12.05782563 q = -12.05782563 Simplifying q = -12.05782563Solution
The solution to the problem is based on the solutions from the subproblems. q = {11.05782563, -12.05782563}
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