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Simplifying 0.5Q2 + 5.5Q = 95 Reorder the terms: 5.5Q + 0.5Q2 = 95 Solving 5.5Q + 0.5Q2 = 95 Solving for variable 'Q'. Reorder the terms: -95 + 5.5Q + 0.5Q2 = 95 + -95 Combine like terms: 95 + -95 = 0 -95 + 5.5Q + 0.5Q2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -190 + 11Q + Q2 = 0 Move the constant term to the right: Add '190' to each side of the equation. -190 + 11Q + 190 + Q2 = 0 + 190 Reorder the terms: -190 + 190 + 11Q + Q2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + 11Q + Q2 = 0 + 190 11Q + Q2 = 0 + 190 Combine like terms: 0 + 190 = 190 11Q + Q2 = 190 The Q term is 11Q. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11Q + 30.25 + Q2 = 190 + 30.25 Reorder the terms: 30.25 + 11Q + Q2 = 190 + 30.25 Combine like terms: 190 + 30.25 = 220.25 30.25 + 11Q + Q2 = 220.25 Factor a perfect square on the left side: (Q + 5.5)(Q + 5.5) = 220.25 Calculate the square root of the right side: 14.84082208 Break this problem into two subproblems by setting (Q + 5.5) equal to 14.84082208 and -14.84082208.Subproblem 1
Q + 5.5 = 14.84082208 Simplifying Q + 5.5 = 14.84082208 Reorder the terms: 5.5 + Q = 14.84082208 Solving 5.5 + Q = 14.84082208 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + Q = 14.84082208 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + Q = 14.84082208 + -5.5 Q = 14.84082208 + -5.5 Combine like terms: 14.84082208 + -5.5 = 9.34082208 Q = 9.34082208 Simplifying Q = 9.34082208Subproblem 2
Q + 5.5 = -14.84082208 Simplifying Q + 5.5 = -14.84082208 Reorder the terms: 5.5 + Q = -14.84082208 Solving 5.5 + Q = -14.84082208 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + Q = -14.84082208 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + Q = -14.84082208 + -5.5 Q = -14.84082208 + -5.5 Combine like terms: -14.84082208 + -5.5 = -20.34082208 Q = -20.34082208 Simplifying Q = -20.34082208Solution
The solution to the problem is based on the solutions from the subproblems. Q = {9.34082208, -20.34082208}
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