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Simplifying -25 = q + -0.2q2 Solving -25 = q + -0.2q2 Solving for variable 'q'. Reorder the terms: -25 + -1q + 0.2q2 = q + -1q + -0.2q2 + 0.2q2 Combine like terms: q + -1q = 0 -25 + -1q + 0.2q2 = 0 + -0.2q2 + 0.2q2 -25 + -1q + 0.2q2 = -0.2q2 + 0.2q2 Combine like terms: -0.2q2 + 0.2q2 = 0.0 -25 + -1q + 0.2q2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -125 + -5q + q2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + -5q + 125 + q2 = 0 + 125 Reorder the terms: -125 + 125 + -5q + q2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -5q + q2 = 0 + 125 -5q + q2 = 0 + 125 Combine like terms: 0 + 125 = 125 -5q + q2 = 125 The q term is -5q. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5q + 6.25 + q2 = 125 + 6.25 Reorder the terms: 6.25 + -5q + q2 = 125 + 6.25 Combine like terms: 125 + 6.25 = 131.25 6.25 + -5q + q2 = 131.25 Factor a perfect square on the left side: (q + -2.5)(q + -2.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (q + -2.5) equal to 11.456439237 and -11.456439237.Subproblem 1
q + -2.5 = 11.456439237 Simplifying q + -2.5 = 11.456439237 Reorder the terms: -2.5 + q = 11.456439237 Solving -2.5 + q = 11.456439237 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + q = 11.456439237 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + q = 11.456439237 + 2.5 q = 11.456439237 + 2.5 Combine like terms: 11.456439237 + 2.5 = 13.956439237 q = 13.956439237 Simplifying q = 13.956439237Subproblem 2
q + -2.5 = -11.456439237 Simplifying q + -2.5 = -11.456439237 Reorder the terms: -2.5 + q = -11.456439237 Solving -2.5 + q = -11.456439237 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + q = -11.456439237 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + q = -11.456439237 + 2.5 q = -11.456439237 + 2.5 Combine like terms: -11.456439237 + 2.5 = -8.956439237 q = -8.956439237 Simplifying q = -8.956439237Solution
The solution to the problem is based on the solutions from the subproblems. q = {13.956439237, -8.956439237}
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