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Simplifying q2 + -15q + -1800 = 0 Reorder the terms: -1800 + -15q + q2 = 0 Solving -1800 + -15q + q2 = 0 Solving for variable 'q'. Begin completing the square. Move the constant term to the right: Add '1800' to each side of the equation. -1800 + -15q + 1800 + q2 = 0 + 1800 Reorder the terms: -1800 + 1800 + -15q + q2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + -15q + q2 = 0 + 1800 -15q + q2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 -15q + q2 = 1800 The q term is -15q. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15q + 56.25 + q2 = 1800 + 56.25 Reorder the terms: 56.25 + -15q + q2 = 1800 + 56.25 Combine like terms: 1800 + 56.25 = 1856.25 56.25 + -15q + q2 = 1856.25 Factor a perfect square on the left side: (q + -7.5)(q + -7.5) = 1856.25 Calculate the square root of the right side: 43.084219849 Break this problem into two subproblems by setting (q + -7.5) equal to 43.084219849 and -43.084219849.Subproblem 1
q + -7.5 = 43.084219849 Simplifying q + -7.5 = 43.084219849 Reorder the terms: -7.5 + q = 43.084219849 Solving -7.5 + q = 43.084219849 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + q = 43.084219849 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + q = 43.084219849 + 7.5 q = 43.084219849 + 7.5 Combine like terms: 43.084219849 + 7.5 = 50.584219849 q = 50.584219849 Simplifying q = 50.584219849Subproblem 2
q + -7.5 = -43.084219849 Simplifying q + -7.5 = -43.084219849 Reorder the terms: -7.5 + q = -43.084219849 Solving -7.5 + q = -43.084219849 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + q = -43.084219849 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + q = -43.084219849 + 7.5 q = -43.084219849 + 7.5 Combine like terms: -43.084219849 + 7.5 = -35.584219849 q = -35.584219849 Simplifying q = -35.584219849Solution
The solution to the problem is based on the solutions from the subproblems. q = {50.584219849, -35.584219849}
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