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Simplifying 8q2 + -42q + -60 = 0 Reorder the terms: -60 + -42q + 8q2 = 0 Solving -60 + -42q + 8q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + -21q + 4q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + -21q + 4q2)' equal to zero and attempt to solve: Simplifying -30 + -21q + 4q2 = 0 Solving -30 + -21q + 4q2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.5 + -5.25q + q2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -5.25q + 7.5 + q2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -5.25q + q2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -5.25q + q2 = 0 + 7.5 -5.25q + q2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -5.25q + q2 = 7.5 The q term is -5.25q. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25q + 6.890625 + q2 = 7.5 + 6.890625 Reorder the terms: 6.890625 + -5.25q + q2 = 7.5 + 6.890625 Combine like terms: 7.5 + 6.890625 = 14.390625 6.890625 + -5.25q + q2 = 14.390625 Factor a perfect square on the left side: (q + -2.625)(q + -2.625) = 14.390625 Calculate the square root of the right side: 3.793497726 Break this problem into two subproblems by setting (q + -2.625) equal to 3.793497726 and -3.793497726.Subproblem 1
q + -2.625 = 3.793497726 Simplifying q + -2.625 = 3.793497726 Reorder the terms: -2.625 + q = 3.793497726 Solving -2.625 + q = 3.793497726 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + q = 3.793497726 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + q = 3.793497726 + 2.625 q = 3.793497726 + 2.625 Combine like terms: 3.793497726 + 2.625 = 6.418497726 q = 6.418497726 Simplifying q = 6.418497726Subproblem 2
q + -2.625 = -3.793497726 Simplifying q + -2.625 = -3.793497726 Reorder the terms: -2.625 + q = -3.793497726 Solving -2.625 + q = -3.793497726 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + q = -3.793497726 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + q = -3.793497726 + 2.625 q = -3.793497726 + 2.625 Combine like terms: -3.793497726 + 2.625 = -1.168497726 q = -1.168497726 Simplifying q = -1.168497726Solution
The solution to the problem is based on the solutions from the subproblems. q = {6.418497726, -1.168497726}Solution
q = {6.418497726, -1.168497726}
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