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Simplifying 2Q2 + Q + -42.9 = 0 Reorder the terms: -42.9 + Q + 2Q2 = 0 Solving -42.9 + Q + 2Q2 = 0 Solving for variable 'Q'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21.45 + 0.5Q + Q2 = 0 Move the constant term to the right: Add '21.45' to each side of the equation. -21.45 + 0.5Q + 21.45 + Q2 = 0 + 21.45 Reorder the terms: -21.45 + 21.45 + 0.5Q + Q2 = 0 + 21.45 Combine like terms: -21.45 + 21.45 = 0.00 0.00 + 0.5Q + Q2 = 0 + 21.45 0.5Q + Q2 = 0 + 21.45 Combine like terms: 0 + 21.45 = 21.45 0.5Q + Q2 = 21.45 The Q term is Q. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5Q + 0.25 + Q2 = 21.45 + 0.25 Reorder the terms: 0.25 + 0.5Q + Q2 = 21.45 + 0.25 Combine like terms: 21.45 + 0.25 = 21.7 0.25 + 0.5Q + Q2 = 21.7 Factor a perfect square on the left side: (Q + 0.5)(Q + 0.5) = 21.7 Calculate the square root of the right side: 4.65832588 Break this problem into two subproblems by setting (Q + 0.5) equal to 4.65832588 and -4.65832588.Subproblem 1
Q + 0.5 = 4.65832588 Simplifying Q + 0.5 = 4.65832588 Reorder the terms: 0.5 + Q = 4.65832588 Solving 0.5 + Q = 4.65832588 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + Q = 4.65832588 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + Q = 4.65832588 + -0.5 Q = 4.65832588 + -0.5 Combine like terms: 4.65832588 + -0.5 = 4.15832588 Q = 4.15832588 Simplifying Q = 4.15832588Subproblem 2
Q + 0.5 = -4.65832588 Simplifying Q + 0.5 = -4.65832588 Reorder the terms: 0.5 + Q = -4.65832588 Solving 0.5 + Q = -4.65832588 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + Q = -4.65832588 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + Q = -4.65832588 + -0.5 Q = -4.65832588 + -0.5 Combine like terms: -4.65832588 + -0.5 = -5.15832588 Q = -5.15832588 Simplifying Q = -5.15832588Solution
The solution to the problem is based on the solutions from the subproblems. Q = {4.15832588, -5.15832588}
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