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Simplifying Q2 + -25Q = 1600 Reorder the terms: -25Q + Q2 = 1600 Solving -25Q + Q2 = 1600 Solving for variable 'Q'. Reorder the terms: -1600 + -25Q + Q2 = 1600 + -1600 Combine like terms: 1600 + -1600 = 0 -1600 + -25Q + Q2 = 0 Begin completing the square. Move the constant term to the right: Add '1600' to each side of the equation. -1600 + -25Q + 1600 + Q2 = 0 + 1600 Reorder the terms: -1600 + 1600 + -25Q + Q2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + -25Q + Q2 = 0 + 1600 -25Q + Q2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 -25Q + Q2 = 1600 The Q term is -25Q. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25Q + 156.25 + Q2 = 1600 + 156.25 Reorder the terms: 156.25 + -25Q + Q2 = 1600 + 156.25 Combine like terms: 1600 + 156.25 = 1756.25 156.25 + -25Q + Q2 = 1756.25 Factor a perfect square on the left side: (Q + -12.5)(Q + -12.5) = 1756.25 Calculate the square root of the right side: 41.907636536 Break this problem into two subproblems by setting (Q + -12.5) equal to 41.907636536 and -41.907636536.Subproblem 1
Q + -12.5 = 41.907636536 Simplifying Q + -12.5 = 41.907636536 Reorder the terms: -12.5 + Q = 41.907636536 Solving -12.5 + Q = 41.907636536 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + Q = 41.907636536 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + Q = 41.907636536 + 12.5 Q = 41.907636536 + 12.5 Combine like terms: 41.907636536 + 12.5 = 54.407636536 Q = 54.407636536 Simplifying Q = 54.407636536Subproblem 2
Q + -12.5 = -41.907636536 Simplifying Q + -12.5 = -41.907636536 Reorder the terms: -12.5 + Q = -41.907636536 Solving -12.5 + Q = -41.907636536 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + Q = -41.907636536 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + Q = -41.907636536 + 12.5 Q = -41.907636536 + 12.5 Combine like terms: -41.907636536 + 12.5 = -29.407636536 Q = -29.407636536 Simplifying Q = -29.407636536Solution
The solution to the problem is based on the solutions from the subproblems. Q = {54.407636536, -29.407636536}
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