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Simplifying Q2 + -3Q = 30 Reorder the terms: -3Q + Q2 = 30 Solving -3Q + Q2 = 30 Solving for variable 'Q'. Reorder the terms: -30 + -3Q + Q2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -3Q + Q2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -3Q + 30 + Q2 = 0 + 30 Reorder the terms: -30 + 30 + -3Q + Q2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -3Q + Q2 = 0 + 30 -3Q + Q2 = 0 + 30 Combine like terms: 0 + 30 = 30 -3Q + Q2 = 30 The Q term is -3Q. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3Q + 2.25 + Q2 = 30 + 2.25 Reorder the terms: 2.25 + -3Q + Q2 = 30 + 2.25 Combine like terms: 30 + 2.25 = 32.25 2.25 + -3Q + Q2 = 32.25 Factor a perfect square on the left side: (Q + -1.5)(Q + -1.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (Q + -1.5) equal to 5.678908346 and -5.678908346.Subproblem 1
Q + -1.5 = 5.678908346 Simplifying Q + -1.5 = 5.678908346 Reorder the terms: -1.5 + Q = 5.678908346 Solving -1.5 + Q = 5.678908346 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + Q = 5.678908346 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + Q = 5.678908346 + 1.5 Q = 5.678908346 + 1.5 Combine like terms: 5.678908346 + 1.5 = 7.178908346 Q = 7.178908346 Simplifying Q = 7.178908346Subproblem 2
Q + -1.5 = -5.678908346 Simplifying Q + -1.5 = -5.678908346 Reorder the terms: -1.5 + Q = -5.678908346 Solving -1.5 + Q = -5.678908346 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + Q = -5.678908346 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + Q = -5.678908346 + 1.5 Q = -5.678908346 + 1.5 Combine like terms: -5.678908346 + 1.5 = -4.178908346 Q = -4.178908346 Simplifying Q = -4.178908346Solution
The solution to the problem is based on the solutions from the subproblems. Q = {7.178908346, -4.178908346}
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