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Simplifying 9(11 + -8q + -2q2) = 0 (11 * 9 + -8q * 9 + -2q2 * 9) = 0 (99 + -72q + -18q2) = 0 Solving 99 + -72q + -18q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '9'. 9(11 + -8q + -2q2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(11 + -8q + -2q2)' equal to zero and attempt to solve: Simplifying 11 + -8q + -2q2 = 0 Solving 11 + -8q + -2q2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5.5 + 4q + q2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 4q + 5.5 + q2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 4q + q2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 4q + q2 = 0 + 5.5 4q + q2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 4q + q2 = 5.5 The q term is 4q. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4q + 4 + q2 = 5.5 + 4 Reorder the terms: 4 + 4q + q2 = 5.5 + 4 Combine like terms: 5.5 + 4 = 9.5 4 + 4q + q2 = 9.5 Factor a perfect square on the left side: (q + 2)(q + 2) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (q + 2) equal to 3.082207001 and -3.082207001.Subproblem 1
q + 2 = 3.082207001 Simplifying q + 2 = 3.082207001 Reorder the terms: 2 + q = 3.082207001 Solving 2 + q = 3.082207001 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + q = 3.082207001 + -2 Combine like terms: 2 + -2 = 0 0 + q = 3.082207001 + -2 q = 3.082207001 + -2 Combine like terms: 3.082207001 + -2 = 1.082207001 q = 1.082207001 Simplifying q = 1.082207001Subproblem 2
q + 2 = -3.082207001 Simplifying q + 2 = -3.082207001 Reorder the terms: 2 + q = -3.082207001 Solving 2 + q = -3.082207001 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + q = -3.082207001 + -2 Combine like terms: 2 + -2 = 0 0 + q = -3.082207001 + -2 q = -3.082207001 + -2 Combine like terms: -3.082207001 + -2 = -5.082207001 q = -5.082207001 Simplifying q = -5.082207001Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.082207001, -5.082207001}Solution
q = {1.082207001, -5.082207001}
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