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Simplifying 40 = 0.012x2 + -0.593x + 35.726 Reorder the terms: 40 = 35.726 + -0.593x + 0.012x2 Solving 40 = 35.726 + -0.593x + 0.012x2 Solving for variable 'x'. Combine like terms: 40 + -35.726 = 4.274 4.274 + 0.593x + -0.012x2 = 35.726 + -0.593x + 0.012x2 + -35.726 + 0.593x + -0.012x2 Reorder the terms: 4.274 + 0.593x + -0.012x2 = 35.726 + -35.726 + -0.593x + 0.593x + 0.012x2 + -0.012x2 Combine like terms: 35.726 + -35.726 = 0.000 4.274 + 0.593x + -0.012x2 = 0.000 + -0.593x + 0.593x + 0.012x2 + -0.012x2 4.274 + 0.593x + -0.012x2 = -0.593x + 0.593x + 0.012x2 + -0.012x2 Combine like terms: -0.593x + 0.593x = 0.000 4.274 + 0.593x + -0.012x2 = 0.000 + 0.012x2 + -0.012x2 4.274 + 0.593x + -0.012x2 = 0.012x2 + -0.012x2 Combine like terms: 0.012x2 + -0.012x2 = 0.000 4.274 + 0.593x + -0.012x2 = 0.000 Begin completing the square. Divide all terms by -0.012 the coefficient of the squared term: Divide each side by '-0.012'. -356.1666667 + -49.41666667x + x2 = 0 Move the constant term to the right: Add '356.1666667' to each side of the equation. -356.1666667 + -49.41666667x + 356.1666667 + x2 = 0 + 356.1666667 Reorder the terms: -356.1666667 + 356.1666667 + -49.41666667x + x2 = 0 + 356.1666667 Combine like terms: -356.1666667 + 356.1666667 = 0.0000000 0.0000000 + -49.41666667x + x2 = 0 + 356.1666667 -49.41666667x + x2 = 0 + 356.1666667 Combine like terms: 0 + 356.1666667 = 356.1666667 -49.41666667x + x2 = 356.1666667 The x term is -49.41666667x. Take half its coefficient (-24.70833334). Square it (610.5017364) and add it to both sides. Add '610.5017364' to each side of the equation. -49.41666667x + 610.5017364 + x2 = 356.1666667 + 610.5017364 Reorder the terms: 610.5017364 + -49.41666667x + x2 = 356.1666667 + 610.5017364 Combine like terms: 356.1666667 + 610.5017364 = 966.6684031 610.5017364 + -49.41666667x + x2 = 966.6684031 Factor a perfect square on the left side: (x + -24.70833334)(x + -24.70833334) = 966.6684031 Calculate the square root of the right side: 31.091291435 Break this problem into two subproblems by setting (x + -24.70833334) equal to 31.091291435 and -31.091291435.Subproblem 1
x + -24.70833334 = 31.091291435 Simplifying x + -24.70833334 = 31.091291435 Reorder the terms: -24.70833334 + x = 31.091291435 Solving -24.70833334 + x = 31.091291435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.70833334' to each side of the equation. -24.70833334 + 24.70833334 + x = 31.091291435 + 24.70833334 Combine like terms: -24.70833334 + 24.70833334 = 0.00000000 0.00000000 + x = 31.091291435 + 24.70833334 x = 31.091291435 + 24.70833334 Combine like terms: 31.091291435 + 24.70833334 = 55.799624775 x = 55.799624775 Simplifying x = 55.799624775Subproblem 2
x + -24.70833334 = -31.091291435 Simplifying x + -24.70833334 = -31.091291435 Reorder the terms: -24.70833334 + x = -31.091291435 Solving -24.70833334 + x = -31.091291435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.70833334' to each side of the equation. -24.70833334 + 24.70833334 + x = -31.091291435 + 24.70833334 Combine like terms: -24.70833334 + 24.70833334 = 0.00000000 0.00000000 + x = -31.091291435 + 24.70833334 x = -31.091291435 + 24.70833334 Combine like terms: -31.091291435 + 24.70833334 = -6.382958095 x = -6.382958095 Simplifying x = -6.382958095Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.799624775, -6.382958095}
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