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Simplifying q(11 + 8q + -2q2) = 0 (11 * q + 8q * q + -2q2 * q) = 0 (11q + 8q2 + -2q3) = 0 Solving 11q + 8q2 + -2q3 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), 'q'. q(11 + 8q + -2q2) = 0Subproblem 1
Set the factor 'q' equal to zero and attempt to solve: Simplifying q = 0 Solving q = 0 Move all terms containing q to the left, all other terms to the right. Simplifying q = 0Subproblem 2
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 = 5.082207001 q = 5.082207001 Simplifying q = 5.082207001Subproblem 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 = -1.082207001 q = -1.082207001 Simplifying q = -1.082207001Solution
The solution to the problem is based on the solutions from the subproblems. q = {5.082207001, -1.082207001}Solution
q = {0, 5.082207001, -1.082207001}
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