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Simplifying -9q2 + -8q + 9 = 0 Reorder the terms: 9 + -8q + -9q2 = 0 Solving 9 + -8q + -9q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1 + 0.8888888889q + q2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.8888888889q + 1 + q2 = 0 + 1 Reorder the terms: -1 + 1 + 0.8888888889q + q2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.8888888889q + q2 = 0 + 1 0.8888888889q + q2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.8888888889q + q2 = 1 The q term is 0.8888888889q. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889q + 0.1975308642 + q2 = 1 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889q + q2 = 1 + 0.1975308642 Combine like terms: 1 + 0.1975308642 = 1.1975308642 0.1975308642 + 0.8888888889q + q2 = 1.1975308642 Factor a perfect square on the left side: (q + 0.4444444445)(q + 0.4444444445) = 1.1975308642 Calculate the square root of the right side: 1.094317534 Break this problem into two subproblems by setting (q + 0.4444444445) equal to 1.094317534 and -1.094317534.Subproblem 1
q + 0.4444444445 = 1.094317534 Simplifying q + 0.4444444445 = 1.094317534 Reorder the terms: 0.4444444445 + q = 1.094317534 Solving 0.4444444445 + q = 1.094317534 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + q = 1.094317534 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + q = 1.094317534 + -0.4444444445 q = 1.094317534 + -0.4444444445 Combine like terms: 1.094317534 + -0.4444444445 = 0.6498730895 q = 0.6498730895 Simplifying q = 0.6498730895Subproblem 2
q + 0.4444444445 = -1.094317534 Simplifying q + 0.4444444445 = -1.094317534 Reorder the terms: 0.4444444445 + q = -1.094317534 Solving 0.4444444445 + q = -1.094317534 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + q = -1.094317534 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + q = -1.094317534 + -0.4444444445 q = -1.094317534 + -0.4444444445 Combine like terms: -1.094317534 + -0.4444444445 = -1.5387619785 q = -1.5387619785 Simplifying q = -1.5387619785Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.6498730895, -1.5387619785}
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