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Simplifying 3000 = 8.121x2 + 6.406x + 257.8 Reorder the terms: 3000 = 257.8 + 6.406x + 8.121x2 Solving 3000 = 257.8 + 6.406x + 8.121x2 Solving for variable 'x'. Combine like terms: 3000 + -257.8 = 2742.2 2742.2 + -6.406x + -8.121x2 = 257.8 + 6.406x + 8.121x2 + -257.8 + -6.406x + -8.121x2 Reorder the terms: 2742.2 + -6.406x + -8.121x2 = 257.8 + -257.8 + 6.406x + -6.406x + 8.121x2 + -8.121x2 Combine like terms: 257.8 + -257.8 = 0.0 2742.2 + -6.406x + -8.121x2 = 0.0 + 6.406x + -6.406x + 8.121x2 + -8.121x2 2742.2 + -6.406x + -8.121x2 = 6.406x + -6.406x + 8.121x2 + -8.121x2 Combine like terms: 6.406x + -6.406x = 0.000 2742.2 + -6.406x + -8.121x2 = 0.000 + 8.121x2 + -8.121x2 2742.2 + -6.406x + -8.121x2 = 8.121x2 + -8.121x2 Combine like terms: 8.121x2 + -8.121x2 = 0.000 2742.2 + -6.406x + -8.121x2 = 0.000 Begin completing the square. Divide all terms by -8.121 the coefficient of the squared term: Divide each side by '-8.121'. -337.6677749 + 0.7888191109x + x2 = 0 Move the constant term to the right: Add '337.6677749' to each side of the equation. -337.6677749 + 0.7888191109x + 337.6677749 + x2 = 0 + 337.6677749 Reorder the terms: -337.6677749 + 337.6677749 + 0.7888191109x + x2 = 0 + 337.6677749 Combine like terms: -337.6677749 + 337.6677749 = 0.0000000 0.0000000 + 0.7888191109x + x2 = 0 + 337.6677749 0.7888191109x + x2 = 0 + 337.6677749 Combine like terms: 0 + 337.6677749 = 337.6677749 0.7888191109x + x2 = 337.6677749 The x term is 0.7888191109x. Take half its coefficient (0.3944095555). Square it (0.1555588975) and add it to both sides. Add '0.1555588975' to each side of the equation. 0.7888191109x + 0.1555588975 + x2 = 337.6677749 + 0.1555588975 Reorder the terms: 0.1555588975 + 0.7888191109x + x2 = 337.6677749 + 0.1555588975 Combine like terms: 337.6677749 + 0.1555588975 = 337.8233337975 0.1555588975 + 0.7888191109x + x2 = 337.8233337975 Factor a perfect square on the left side: (x + 0.3944095555)(x + 0.3944095555) = 337.8233337975 Calculate the square root of the right side: 18.379970996 Break this problem into two subproblems by setting (x + 0.3944095555) equal to 18.379970996 and -18.379970996.Subproblem 1
x + 0.3944095555 = 18.379970996 Simplifying x + 0.3944095555 = 18.379970996 Reorder the terms: 0.3944095555 + x = 18.379970996 Solving 0.3944095555 + x = 18.379970996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3944095555' to each side of the equation. 0.3944095555 + -0.3944095555 + x = 18.379970996 + -0.3944095555 Combine like terms: 0.3944095555 + -0.3944095555 = 0.0000000000 0.0000000000 + x = 18.379970996 + -0.3944095555 x = 18.379970996 + -0.3944095555 Combine like terms: 18.379970996 + -0.3944095555 = 17.9855614405 x = 17.9855614405 Simplifying x = 17.9855614405Subproblem 2
x + 0.3944095555 = -18.379970996 Simplifying x + 0.3944095555 = -18.379970996 Reorder the terms: 0.3944095555 + x = -18.379970996 Solving 0.3944095555 + x = -18.379970996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3944095555' to each side of the equation. 0.3944095555 + -0.3944095555 + x = -18.379970996 + -0.3944095555 Combine like terms: 0.3944095555 + -0.3944095555 = 0.0000000000 0.0000000000 + x = -18.379970996 + -0.3944095555 x = -18.379970996 + -0.3944095555 Combine like terms: -18.379970996 + -0.3944095555 = -18.7743805515 x = -18.7743805515 Simplifying x = -18.7743805515Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.9855614405, -18.7743805515}
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