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Simplifying q2 + 72 = 20q Reorder the terms: 72 + q2 = 20q Solving 72 + q2 = 20q Solving for variable 'q'. Reorder the terms: 72 + -20q + q2 = 20q + -20q Combine like terms: 20q + -20q = 0 72 + -20q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -20q + -72 + q2 = 0 + -72 Reorder the terms: 72 + -72 + -20q + q2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -20q + q2 = 0 + -72 -20q + q2 = 0 + -72 Combine like terms: 0 + -72 = -72 -20q + q2 = -72 The q term is -20q. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20q + 100 + q2 = -72 + 100 Reorder the terms: 100 + -20q + q2 = -72 + 100 Combine like terms: -72 + 100 = 28 100 + -20q + q2 = 28 Factor a perfect square on the left side: (q + -10)(q + -10) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (q + -10) equal to 5.291502622 and -5.291502622.Subproblem 1
q + -10 = 5.291502622 Simplifying q + -10 = 5.291502622 Reorder the terms: -10 + q = 5.291502622 Solving -10 + q = 5.291502622 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + q = 5.291502622 + 10 Combine like terms: -10 + 10 = 0 0 + q = 5.291502622 + 10 q = 5.291502622 + 10 Combine like terms: 5.291502622 + 10 = 15.291502622 q = 15.291502622 Simplifying q = 15.291502622Subproblem 2
q + -10 = -5.291502622 Simplifying q + -10 = -5.291502622 Reorder the terms: -10 + q = -5.291502622 Solving -10 + q = -5.291502622 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + q = -5.291502622 + 10 Combine like terms: -10 + 10 = 0 0 + q = -5.291502622 + 10 q = -5.291502622 + 10 Combine like terms: -5.291502622 + 10 = 4.708497378 q = 4.708497378 Simplifying q = 4.708497378Solution
The solution to the problem is based on the solutions from the subproblems. q = {15.291502622, 4.708497378}
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