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Simplifying 155 = -0.1Q2 + 10Q + -90 Reorder the terms: 155 = -90 + 10Q + -0.1Q2 Solving 155 = -90 + 10Q + -0.1Q2 Solving for variable 'Q'. Combine like terms: 155 + 90 = 245 245 + -10Q + 0.1Q2 = -90 + 10Q + -0.1Q2 + 90 + -10Q + 0.1Q2 Reorder the terms: 245 + -10Q + 0.1Q2 = -90 + 90 + 10Q + -10Q + -0.1Q2 + 0.1Q2 Combine like terms: -90 + 90 = 0 245 + -10Q + 0.1Q2 = 0 + 10Q + -10Q + -0.1Q2 + 0.1Q2 245 + -10Q + 0.1Q2 = 10Q + -10Q + -0.1Q2 + 0.1Q2 Combine like terms: 10Q + -10Q = 0 245 + -10Q + 0.1Q2 = 0 + -0.1Q2 + 0.1Q2 245 + -10Q + 0.1Q2 = -0.1Q2 + 0.1Q2 Combine like terms: -0.1Q2 + 0.1Q2 = 0.0 245 + -10Q + 0.1Q2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 2450 + -100Q + Q2 = 0 Move the constant term to the right: Add '-2450' to each side of the equation. 2450 + -100Q + -2450 + Q2 = 0 + -2450 Reorder the terms: 2450 + -2450 + -100Q + Q2 = 0 + -2450 Combine like terms: 2450 + -2450 = 0 0 + -100Q + Q2 = 0 + -2450 -100Q + Q2 = 0 + -2450 Combine like terms: 0 + -2450 = -2450 -100Q + Q2 = -2450 The Q term is -100Q. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100Q + 2500 + Q2 = -2450 + 2500 Reorder the terms: 2500 + -100Q + Q2 = -2450 + 2500 Combine like terms: -2450 + 2500 = 50 2500 + -100Q + Q2 = 50 Factor a perfect square on the left side: (Q + -50)(Q + -50) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (Q + -50) equal to 7.071067812 and -7.071067812.Subproblem 1
Q + -50 = 7.071067812 Simplifying Q + -50 = 7.071067812 Reorder the terms: -50 + Q = 7.071067812 Solving -50 + Q = 7.071067812 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + Q = 7.071067812 + 50 Combine like terms: -50 + 50 = 0 0 + Q = 7.071067812 + 50 Q = 7.071067812 + 50 Combine like terms: 7.071067812 + 50 = 57.071067812 Q = 57.071067812 Simplifying Q = 57.071067812Subproblem 2
Q + -50 = -7.071067812 Simplifying Q + -50 = -7.071067812 Reorder the terms: -50 + Q = -7.071067812 Solving -50 + Q = -7.071067812 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + Q = -7.071067812 + 50 Combine like terms: -50 + 50 = 0 0 + Q = -7.071067812 + 50 Q = -7.071067812 + 50 Combine like terms: -7.071067812 + 50 = 42.928932188 Q = 42.928932188 Simplifying Q = 42.928932188Solution
The solution to the problem is based on the solutions from the subproblems. Q = {57.071067812, 42.928932188}
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