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Simplifying -2q2 + -28q = -86 Reorder the terms: -28q + -2q2 = -86 Solving -28q + -2q2 = -86 Solving for variable 'q'. Reorder the terms: 86 + -28q + -2q2 = -86 + 86 Combine like terms: -86 + 86 = 0 86 + -28q + -2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(43 + -14q + -1q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(43 + -14q + -1q2)' equal to zero and attempt to solve: Simplifying 43 + -14q + -1q2 = 0 Solving 43 + -14q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -43 + 14q + q2 = 0 Move the constant term to the right: Add '43' to each side of the equation. -43 + 14q + 43 + q2 = 0 + 43 Reorder the terms: -43 + 43 + 14q + q2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 14q + q2 = 0 + 43 14q + q2 = 0 + 43 Combine like terms: 0 + 43 = 43 14q + q2 = 43 The q term is 14q. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14q + 49 + q2 = 43 + 49 Reorder the terms: 49 + 14q + q2 = 43 + 49 Combine like terms: 43 + 49 = 92 49 + 14q + q2 = 92 Factor a perfect square on the left side: (q + 7)(q + 7) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (q + 7) equal to 9.591663047 and -9.591663047.Subproblem 1
q + 7 = 9.591663047 Simplifying q + 7 = 9.591663047 Reorder the terms: 7 + q = 9.591663047 Solving 7 + q = 9.591663047 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + q = 9.591663047 + -7 Combine like terms: 7 + -7 = 0 0 + q = 9.591663047 + -7 q = 9.591663047 + -7 Combine like terms: 9.591663047 + -7 = 2.591663047 q = 2.591663047 Simplifying q = 2.591663047Subproblem 2
q + 7 = -9.591663047 Simplifying q + 7 = -9.591663047 Reorder the terms: 7 + q = -9.591663047 Solving 7 + q = -9.591663047 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + q = -9.591663047 + -7 Combine like terms: 7 + -7 = 0 0 + q = -9.591663047 + -7 q = -9.591663047 + -7 Combine like terms: -9.591663047 + -7 = -16.591663047 q = -16.591663047 Simplifying q = -16.591663047Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.591663047, -16.591663047}Solution
q = {2.591663047, -16.591663047}
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