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Simplifying 250 + -1Q2 = 4Q Solving 250 + -1Q2 = 4Q Solving for variable 'Q'. Reorder the terms: 250 + -4Q + -1Q2 = 4Q + -4Q Combine like terms: 4Q + -4Q = 0 250 + -4Q + -1Q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -250 + 4Q + Q2 = 0 Move the constant term to the right: Add '250' to each side of the equation. -250 + 4Q + 250 + Q2 = 0 + 250 Reorder the terms: -250 + 250 + 4Q + Q2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 4Q + Q2 = 0 + 250 4Q + Q2 = 0 + 250 Combine like terms: 0 + 250 = 250 4Q + Q2 = 250 The Q term is 4Q. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4Q + 4 + Q2 = 250 + 4 Reorder the terms: 4 + 4Q + Q2 = 250 + 4 Combine like terms: 250 + 4 = 254 4 + 4Q + Q2 = 254 Factor a perfect square on the left side: (Q + 2)(Q + 2) = 254 Calculate the square root of the right side: 15.937377451 Break this problem into two subproblems by setting (Q + 2) equal to 15.937377451 and -15.937377451.Subproblem 1
Q + 2 = 15.937377451 Simplifying Q + 2 = 15.937377451 Reorder the terms: 2 + Q = 15.937377451 Solving 2 + Q = 15.937377451 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + Q = 15.937377451 + -2 Combine like terms: 2 + -2 = 0 0 + Q = 15.937377451 + -2 Q = 15.937377451 + -2 Combine like terms: 15.937377451 + -2 = 13.937377451 Q = 13.937377451 Simplifying Q = 13.937377451Subproblem 2
Q + 2 = -15.937377451 Simplifying Q + 2 = -15.937377451 Reorder the terms: 2 + Q = -15.937377451 Solving 2 + Q = -15.937377451 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + Q = -15.937377451 + -2 Combine like terms: 2 + -2 = 0 0 + Q = -15.937377451 + -2 Q = -15.937377451 + -2 Combine like terms: -15.937377451 + -2 = -17.937377451 Q = -17.937377451 Simplifying Q = -17.937377451Solution
The solution to the problem is based on the solutions from the subproblems. Q = {13.937377451, -17.937377451}
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