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Simplifying 11q2 + -21q + -20 = 0 Reorder the terms: -20 + -21q + 11q2 = 0 Solving -20 + -21q + 11q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.818181818 + -1.909090909q + q2 = 0 Move the constant term to the right: Add '1.818181818' to each side of the equation. -1.818181818 + -1.909090909q + 1.818181818 + q2 = 0 + 1.818181818 Reorder the terms: -1.818181818 + 1.818181818 + -1.909090909q + q2 = 0 + 1.818181818 Combine like terms: -1.818181818 + 1.818181818 = 0.000000000 0.000000000 + -1.909090909q + q2 = 0 + 1.818181818 -1.909090909q + q2 = 0 + 1.818181818 Combine like terms: 0 + 1.818181818 = 1.818181818 -1.909090909q + q2 = 1.818181818 The q term is -1.909090909q. Take half its coefficient (-0.9545454545). Square it (0.9111570247) and add it to both sides. Add '0.9111570247' to each side of the equation. -1.909090909q + 0.9111570247 + q2 = 1.818181818 + 0.9111570247 Reorder the terms: 0.9111570247 + -1.909090909q + q2 = 1.818181818 + 0.9111570247 Combine like terms: 1.818181818 + 0.9111570247 = 2.7293388427 0.9111570247 + -1.909090909q + q2 = 2.7293388427 Factor a perfect square on the left side: (q + -0.9545454545)(q + -0.9545454545) = 2.7293388427 Calculate the square root of the right side: 1.652071077 Break this problem into two subproblems by setting (q + -0.9545454545) equal to 1.652071077 and -1.652071077.Subproblem 1
q + -0.9545454545 = 1.652071077 Simplifying q + -0.9545454545 = 1.652071077 Reorder the terms: -0.9545454545 + q = 1.652071077 Solving -0.9545454545 + q = 1.652071077 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.9545454545' to each side of the equation. -0.9545454545 + 0.9545454545 + q = 1.652071077 + 0.9545454545 Combine like terms: -0.9545454545 + 0.9545454545 = 0.0000000000 0.0000000000 + q = 1.652071077 + 0.9545454545 q = 1.652071077 + 0.9545454545 Combine like terms: 1.652071077 + 0.9545454545 = 2.6066165315 q = 2.6066165315 Simplifying q = 2.6066165315Subproblem 2
q + -0.9545454545 = -1.652071077 Simplifying q + -0.9545454545 = -1.652071077 Reorder the terms: -0.9545454545 + q = -1.652071077 Solving -0.9545454545 + q = -1.652071077 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.9545454545' to each side of the equation. -0.9545454545 + 0.9545454545 + q = -1.652071077 + 0.9545454545 Combine like terms: -0.9545454545 + 0.9545454545 = 0.0000000000 0.0000000000 + q = -1.652071077 + 0.9545454545 q = -1.652071077 + 0.9545454545 Combine like terms: -1.652071077 + 0.9545454545 = -0.6975256225 q = -0.6975256225 Simplifying q = -0.6975256225Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.6066165315, -0.6975256225}
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