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Simplifying q2 + 75q + -6250 = q Reorder the terms: -6250 + 75q + q2 = q Solving -6250 + 75q + q2 = q Solving for variable 'q'. Reorder the terms: -6250 + 75q + -1q + q2 = q + -1q Combine like terms: 75q + -1q = 74q -6250 + 74q + q2 = q + -1q Combine like terms: q + -1q = 0 -6250 + 74q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '6250' to each side of the equation. -6250 + 74q + 6250 + q2 = 0 + 6250 Reorder the terms: -6250 + 6250 + 74q + q2 = 0 + 6250 Combine like terms: -6250 + 6250 = 0 0 + 74q + q2 = 0 + 6250 74q + q2 = 0 + 6250 Combine like terms: 0 + 6250 = 6250 74q + q2 = 6250 The q term is 74q. Take half its coefficient (37). Square it (1369) and add it to both sides. Add '1369' to each side of the equation. 74q + 1369 + q2 = 6250 + 1369 Reorder the terms: 1369 + 74q + q2 = 6250 + 1369 Combine like terms: 6250 + 1369 = 7619 1369 + 74q + q2 = 7619 Factor a perfect square on the left side: (q + 37)(q + 37) = 7619 Calculate the square root of the right side: 87.286883322 Break this problem into two subproblems by setting (q + 37) equal to 87.286883322 and -87.286883322.Subproblem 1
q + 37 = 87.286883322 Simplifying q + 37 = 87.286883322 Reorder the terms: 37 + q = 87.286883322 Solving 37 + q = 87.286883322 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + q = 87.286883322 + -37 Combine like terms: 37 + -37 = 0 0 + q = 87.286883322 + -37 q = 87.286883322 + -37 Combine like terms: 87.286883322 + -37 = 50.286883322 q = 50.286883322 Simplifying q = 50.286883322Subproblem 2
q + 37 = -87.286883322 Simplifying q + 37 = -87.286883322 Reorder the terms: 37 + q = -87.286883322 Solving 37 + q = -87.286883322 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + q = -87.286883322 + -37 Combine like terms: 37 + -37 = 0 0 + q = -87.286883322 + -37 q = -87.286883322 + -37 Combine like terms: -87.286883322 + -37 = -124.286883322 q = -124.286883322 Simplifying q = -124.286883322Solution
The solution to the problem is based on the solutions from the subproblems. q = {50.286883322, -124.286883322}
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