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Simplifying -9q2 + -9q + 8 = 0 Reorder the terms: 8 + -9q + -9q2 = 0 Solving 8 + -9q + -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'. -0.8888888889 + q + q2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + q + 0.8888888889 + q2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + q + q2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + q + q2 = 0 + 0.8888888889 q + q2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 q + q2 = 0.8888888889 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. + 0.25 + q2 = 0.8888888889 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + q2 = 0.8888888889 + 0.25 Combine like terms: 0.8888888889 + 0.25 = 1.1388888889 1.25 + q2 = 1.1388888889 Factor a perfect square on the left side: (q + 0.5)(q + 0.5) = 1.1388888889 Calculate the square root of the right side: 1.067187373 Break this problem into two subproblems by setting (q + 0.5) equal to 1.067187373 and -1.067187373.Subproblem 1
q + 0.5 = 1.067187373 Simplifying q + 0.5 = 1.067187373 Reorder the terms: 0.5 + q = 1.067187373 Solving 0.5 + q = 1.067187373 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 = 1.067187373 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = 1.067187373 + -0.5 q = 1.067187373 + -0.5 Combine like terms: 1.067187373 + -0.5 = 0.567187373 q = 0.567187373 Simplifying q = 0.567187373Subproblem 2
q + 0.5 = -1.067187373 Simplifying q + 0.5 = -1.067187373 Reorder the terms: 0.5 + q = -1.067187373 Solving 0.5 + q = -1.067187373 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 = -1.067187373 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + q = -1.067187373 + -0.5 q = -1.067187373 + -0.5 Combine like terms: -1.067187373 + -0.5 = -1.567187373 q = -1.567187373 Simplifying q = -1.567187373Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.567187373, -1.567187373}
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