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Simplifying 0.0163212q2 + -551q + -160000000 = 0 Reorder the terms: -160000000 + -551q + 0.0163212q2 = 0 Solving -160000000 + -551q + 0.0163212q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 0.0163212 the coefficient of the squared term: Divide each side by '0.0163212'. -9803200745 + -33759.77257q + q2 = 0 Move the constant term to the right: Add '9803200745' to each side of the equation. -9803200745 + -33759.77257q + 9803200745 + q2 = 0 + 9803200745 Reorder the terms: -9803200745 + 9803200745 + -33759.77257q + q2 = 0 + 9803200745 Combine like terms: -9803200745 + 9803200745 = 0 0 + -33759.77257q + q2 = 0 + 9803200745 -33759.77257q + q2 = 0 + 9803200745 Combine like terms: 0 + 9803200745 = 9803200745 -33759.77257q + q2 = 9803200745 The q term is -33759.77257q. Take half its coefficient (-16879.88629). Square it (284930561.2) and add it to both sides. Add '284930561.2' to each side of the equation. -33759.77257q + 284930561.2 + q2 = 9803200745 + 284930561.2 Reorder the terms: 284930561.2 + -33759.77257q + q2 = 9803200745 + 284930561.2 Combine like terms: 9803200745 + 284930561.2 = 10088131306.2 284930561.2 + -33759.77257q + q2 = 10088131306.2 Factor a perfect square on the left side: (q + -16879.88629)(q + -16879.88629) = 10088131306.2 Calculate the square root of the right side: 100439.689894981 Break this problem into two subproblems by setting (q + -16879.88629) equal to 100439.689894981 and -100439.689894981.Subproblem 1
q + -16879.88629 = 100439.689894981 Simplifying q + -16879.88629 = 100439.689894981 Reorder the terms: -16879.88629 + q = 100439.689894981 Solving -16879.88629 + q = 100439.689894981 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '16879.88629' to each side of the equation. -16879.88629 + 16879.88629 + q = 100439.689894981 + 16879.88629 Combine like terms: -16879.88629 + 16879.88629 = 0.00000 0.00000 + q = 100439.689894981 + 16879.88629 q = 100439.689894981 + 16879.88629 Combine like terms: 100439.689894981 + 16879.88629 = 117319.576184981 q = 117319.576184981 Simplifying q = 117319.576184981Subproblem 2
q + -16879.88629 = -100439.689894981 Simplifying q + -16879.88629 = -100439.689894981 Reorder the terms: -16879.88629 + q = -100439.689894981 Solving -16879.88629 + q = -100439.689894981 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '16879.88629' to each side of the equation. -16879.88629 + 16879.88629 + q = -100439.689894981 + 16879.88629 Combine like terms: -16879.88629 + 16879.88629 = 0.00000 0.00000 + q = -100439.689894981 + 16879.88629 q = -100439.689894981 + 16879.88629 Combine like terms: -100439.689894981 + 16879.88629 = -83559.803604981 q = -83559.803604981 Simplifying q = -83559.803604981Solution
The solution to the problem is based on the solutions from the subproblems. q = {117319.576184981, -83559.803604981}
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