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Simplifying 6q + q2 = 7200 Solving 6q + q2 = 7200 Solving for variable 'q'. Reorder the terms: -7200 + 6q + q2 = 7200 + -7200 Combine like terms: 7200 + -7200 = 0 -7200 + 6q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '7200' to each side of the equation. -7200 + 6q + 7200 + q2 = 0 + 7200 Reorder the terms: -7200 + 7200 + 6q + q2 = 0 + 7200 Combine like terms: -7200 + 7200 = 0 0 + 6q + q2 = 0 + 7200 6q + q2 = 0 + 7200 Combine like terms: 0 + 7200 = 7200 6q + q2 = 7200 The q term is 6q. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6q + 9 + q2 = 7200 + 9 Reorder the terms: 9 + 6q + q2 = 7200 + 9 Combine like terms: 7200 + 9 = 7209 9 + 6q + q2 = 7209 Factor a perfect square on the left side: (q + 3)(q + 3) = 7209 Calculate the square root of the right side: 84.905830189 Break this problem into two subproblems by setting (q + 3) equal to 84.905830189 and -84.905830189.Subproblem 1
q + 3 = 84.905830189 Simplifying q + 3 = 84.905830189 Reorder the terms: 3 + q = 84.905830189 Solving 3 + q = 84.905830189 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + q = 84.905830189 + -3 Combine like terms: 3 + -3 = 0 0 + q = 84.905830189 + -3 q = 84.905830189 + -3 Combine like terms: 84.905830189 + -3 = 81.905830189 q = 81.905830189 Simplifying q = 81.905830189Subproblem 2
q + 3 = -84.905830189 Simplifying q + 3 = -84.905830189 Reorder the terms: 3 + q = -84.905830189 Solving 3 + q = -84.905830189 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + q = -84.905830189 + -3 Combine like terms: 3 + -3 = 0 0 + q = -84.905830189 + -3 q = -84.905830189 + -3 Combine like terms: -84.905830189 + -3 = -87.905830189 q = -87.905830189 Simplifying q = -87.905830189Solution
The solution to the problem is based on the solutions from the subproblems. q = {81.905830189, -87.905830189}
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