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Simplifying 1381 = -2.05x2 + 77.85x + 742 Reorder the terms: 1381 = 742 + 77.85x + -2.05x2 Solving 1381 = 742 + 77.85x + -2.05x2 Solving for variable 'x'. Combine like terms: 1381 + -742 = 639 639 + -77.85x + 2.05x2 = 742 + 77.85x + -2.05x2 + -742 + -77.85x + 2.05x2 Reorder the terms: 639 + -77.85x + 2.05x2 = 742 + -742 + 77.85x + -77.85x + -2.05x2 + 2.05x2 Combine like terms: 742 + -742 = 0 639 + -77.85x + 2.05x2 = 0 + 77.85x + -77.85x + -2.05x2 + 2.05x2 639 + -77.85x + 2.05x2 = 77.85x + -77.85x + -2.05x2 + 2.05x2 Combine like terms: 77.85x + -77.85x = 0.00 639 + -77.85x + 2.05x2 = 0.00 + -2.05x2 + 2.05x2 639 + -77.85x + 2.05x2 = -2.05x2 + 2.05x2 Combine like terms: -2.05x2 + 2.05x2 = 0.00 639 + -77.85x + 2.05x2 = 0.00 Begin completing the square. Divide all terms by 2.05 the coefficient of the squared term: Divide each side by '2.05'. 311.7073171 + -37.97560976x + x2 = 0 Move the constant term to the right: Add '-311.7073171' to each side of the equation. 311.7073171 + -37.97560976x + -311.7073171 + x2 = 0 + -311.7073171 Reorder the terms: 311.7073171 + -311.7073171 + -37.97560976x + x2 = 0 + -311.7073171 Combine like terms: 311.7073171 + -311.7073171 = 0.0000000 0.0000000 + -37.97560976x + x2 = 0 + -311.7073171 -37.97560976x + x2 = 0 + -311.7073171 Combine like terms: 0 + -311.7073171 = -311.7073171 -37.97560976x + x2 = -311.7073171 The x term is -37.97560976x. Take half its coefficient (-18.98780488). Square it (360.5367342) and add it to both sides. Add '360.5367342' to each side of the equation. -37.97560976x + 360.5367342 + x2 = -311.7073171 + 360.5367342 Reorder the terms: 360.5367342 + -37.97560976x + x2 = -311.7073171 + 360.5367342 Combine like terms: -311.7073171 + 360.5367342 = 48.8294171 360.5367342 + -37.97560976x + x2 = 48.8294171 Factor a perfect square on the left side: (x + -18.98780488)(x + -18.98780488) = 48.8294171 Calculate the square root of the right side: 6.987804884 Break this problem into two subproblems by setting (x + -18.98780488) equal to 6.987804884 and -6.987804884.Subproblem 1
x + -18.98780488 = 6.987804884 Simplifying x + -18.98780488 = 6.987804884 Reorder the terms: -18.98780488 + x = 6.987804884 Solving -18.98780488 + x = 6.987804884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.98780488' to each side of the equation. -18.98780488 + 18.98780488 + x = 6.987804884 + 18.98780488 Combine like terms: -18.98780488 + 18.98780488 = 0.00000000 0.00000000 + x = 6.987804884 + 18.98780488 x = 6.987804884 + 18.98780488 Combine like terms: 6.987804884 + 18.98780488 = 25.975609764 x = 25.975609764 Simplifying x = 25.975609764Subproblem 2
x + -18.98780488 = -6.987804884 Simplifying x + -18.98780488 = -6.987804884 Reorder the terms: -18.98780488 + x = -6.987804884 Solving -18.98780488 + x = -6.987804884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.98780488' to each side of the equation. -18.98780488 + 18.98780488 + x = -6.987804884 + 18.98780488 Combine like terms: -18.98780488 + 18.98780488 = 0.00000000 0.00000000 + x = -6.987804884 + 18.98780488 x = -6.987804884 + 18.98780488 Combine like terms: -6.987804884 + 18.98780488 = 11.999999996 x = 11.999999996 Simplifying x = 11.999999996Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.975609764, 11.999999996}
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