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Simplifying q2 + -12q = 20 Reorder the terms: -12q + q2 = 20 Solving -12q + q2 = 20 Solving for variable 'q'. Reorder the terms: -20 + -12q + q2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -12q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -12q + 20 + q2 = 0 + 20 Reorder the terms: -20 + 20 + -12q + q2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -12q + q2 = 0 + 20 -12q + q2 = 0 + 20 Combine like terms: 0 + 20 = 20 -12q + q2 = 20 The q term is -12q. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12q + 36 + q2 = 20 + 36 Reorder the terms: 36 + -12q + q2 = 20 + 36 Combine like terms: 20 + 36 = 56 36 + -12q + q2 = 56 Factor a perfect square on the left side: (q + -6)(q + -6) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (q + -6) equal to 7.483314774 and -7.483314774.Subproblem 1
q + -6 = 7.483314774 Simplifying q + -6 = 7.483314774 Reorder the terms: -6 + q = 7.483314774 Solving -6 + q = 7.483314774 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + q = 7.483314774 + 6 Combine like terms: -6 + 6 = 0 0 + q = 7.483314774 + 6 q = 7.483314774 + 6 Combine like terms: 7.483314774 + 6 = 13.483314774 q = 13.483314774 Simplifying q = 13.483314774Subproblem 2
q + -6 = -7.483314774 Simplifying q + -6 = -7.483314774 Reorder the terms: -6 + q = -7.483314774 Solving -6 + q = -7.483314774 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + q = -7.483314774 + 6 Combine like terms: -6 + 6 = 0 0 + q = -7.483314774 + 6 q = -7.483314774 + 6 Combine like terms: -7.483314774 + 6 = -1.483314774 q = -1.483314774 Simplifying q = -1.483314774Solution
The solution to the problem is based on the solutions from the subproblems. q = {13.483314774, -1.483314774}
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