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Simplifying -0.0399x2 + -2x + 75 = 0 Reorder the terms: 75 + -2x + -0.0399x2 = 0 Solving 75 + -2x + -0.0399x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0399 the coefficient of the squared term: Divide each side by '-0.0399'. -1879.699248 + 50.12531328x + x2 = 0 Move the constant term to the right: Add '1879.699248' to each side of the equation. -1879.699248 + 50.12531328x + 1879.699248 + x2 = 0 + 1879.699248 Reorder the terms: -1879.699248 + 1879.699248 + 50.12531328x + x2 = 0 + 1879.699248 Combine like terms: -1879.699248 + 1879.699248 = 0.000000 0.000000 + 50.12531328x + x2 = 0 + 1879.699248 50.12531328x + x2 = 0 + 1879.699248 Combine like terms: 0 + 1879.699248 = 1879.699248 50.12531328x + x2 = 1879.699248 The x term is 50.12531328x. Take half its coefficient (25.06265664). Square it (628.1367579) and add it to both sides. Add '628.1367579' to each side of the equation. 50.12531328x + 628.1367579 + x2 = 1879.699248 + 628.1367579 Reorder the terms: 628.1367579 + 50.12531328x + x2 = 1879.699248 + 628.1367579 Combine like terms: 1879.699248 + 628.1367579 = 2507.8360059 628.1367579 + 50.12531328x + x2 = 2507.8360059 Factor a perfect square on the left side: (x + 25.06265664)(x + 25.06265664) = 2507.8360059 Calculate the square root of the right side: 50.078298752 Break this problem into two subproblems by setting (x + 25.06265664) equal to 50.078298752 and -50.078298752.Subproblem 1
x + 25.06265664 = 50.078298752 Simplifying x + 25.06265664 = 50.078298752 Reorder the terms: 25.06265664 + x = 50.078298752 Solving 25.06265664 + x = 50.078298752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.06265664' to each side of the equation. 25.06265664 + -25.06265664 + x = 50.078298752 + -25.06265664 Combine like terms: 25.06265664 + -25.06265664 = 0.00000000 0.00000000 + x = 50.078298752 + -25.06265664 x = 50.078298752 + -25.06265664 Combine like terms: 50.078298752 + -25.06265664 = 25.015642112 x = 25.015642112 Simplifying x = 25.015642112Subproblem 2
x + 25.06265664 = -50.078298752 Simplifying x + 25.06265664 = -50.078298752 Reorder the terms: 25.06265664 + x = -50.078298752 Solving 25.06265664 + x = -50.078298752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.06265664' to each side of the equation. 25.06265664 + -25.06265664 + x = -50.078298752 + -25.06265664 Combine like terms: 25.06265664 + -25.06265664 = 0.00000000 0.00000000 + x = -50.078298752 + -25.06265664 x = -50.078298752 + -25.06265664 Combine like terms: -50.078298752 + -25.06265664 = -75.140955392 x = -75.140955392 Simplifying x = -75.140955392Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.015642112, -75.140955392}
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