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Simplifying 8q2 + 6q + -6 = 0 Reorder the terms: -6 + 6q + 8q2 = 0 Solving -6 + 6q + 8q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 3q + 4q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 3q + 4q2)' equal to zero and attempt to solve: Simplifying -3 + 3q + 4q2 = 0 Solving -3 + 3q + 4q2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 0.75q + q2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.75q + 0.75 + q2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.75q + q2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.75q + q2 = 0 + 0.75 0.75q + q2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.75q + q2 = 0.75 The q term is 0.75q. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75q + 0.140625 + q2 = 0.75 + 0.140625 Reorder the terms: 0.140625 + 0.75q + q2 = 0.75 + 0.140625 Combine like terms: 0.75 + 0.140625 = 0.890625 0.140625 + 0.75q + q2 = 0.890625 Factor a perfect square on the left side: (q + 0.375)(q + 0.375) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (q + 0.375) equal to 0.943729304 and -0.943729304.Subproblem 1
q + 0.375 = 0.943729304 Simplifying q + 0.375 = 0.943729304 Reorder the terms: 0.375 + q = 0.943729304 Solving 0.375 + q = 0.943729304 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + q = 0.943729304 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + q = 0.943729304 + -0.375 q = 0.943729304 + -0.375 Combine like terms: 0.943729304 + -0.375 = 0.568729304 q = 0.568729304 Simplifying q = 0.568729304Subproblem 2
q + 0.375 = -0.943729304 Simplifying q + 0.375 = -0.943729304 Reorder the terms: 0.375 + q = -0.943729304 Solving 0.375 + q = -0.943729304 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + q = -0.943729304 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + q = -0.943729304 + -0.375 q = -0.943729304 + -0.375 Combine like terms: -0.943729304 + -0.375 = -1.318729304 q = -1.318729304 Simplifying q = -1.318729304Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.568729304, -1.318729304}Solution
q = {0.568729304, -1.318729304}
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