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Simplifying 0.0399x2 + x + -75 = 0 Reorder the terms: -75 + x + 0.0399x2 = 0 Solving -75 + x + 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 + 25.06265664x + x2 = 0 Move the constant term to the right: Add '1879.699248' to each side of the equation. -1879.699248 + 25.06265664x + 1879.699248 + x2 = 0 + 1879.699248 Reorder the terms: -1879.699248 + 1879.699248 + 25.06265664x + x2 = 0 + 1879.699248 Combine like terms: -1879.699248 + 1879.699248 = 0.000000 0.000000 + 25.06265664x + x2 = 0 + 1879.699248 25.06265664x + x2 = 0 + 1879.699248 Combine like terms: 0 + 1879.699248 = 1879.699248 25.06265664x + x2 = 1879.699248 The x term is x. 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. 25.06265664x + 0.25 + x2 = 1879.699248 + 0.25 Reorder the terms: 0.25 + 25.06265664x + x2 = 1879.699248 + 0.25 Combine like terms: 1879.699248 + 0.25 = 1879.949248 0.25 + 25.06265664x + x2 = 1879.949248 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1879.949248 Calculate the square root of the right side: 43.35838152 Break this problem into two subproblems by setting (x + 0.5) equal to 43.35838152 and -43.35838152.Subproblem 1
x + 0.5 = 43.35838152 Simplifying x + 0.5 = 43.35838152 Reorder the terms: 0.5 + x = 43.35838152 Solving 0.5 + x = 43.35838152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 43.35838152 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 43.35838152 + -0.5 x = 43.35838152 + -0.5 Combine like terms: 43.35838152 + -0.5 = 42.85838152 x = 42.85838152 Simplifying x = 42.85838152Subproblem 2
x + 0.5 = -43.35838152 Simplifying x + 0.5 = -43.35838152 Reorder the terms: 0.5 + x = -43.35838152 Solving 0.5 + x = -43.35838152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -43.35838152 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -43.35838152 + -0.5 x = -43.35838152 + -0.5 Combine like terms: -43.35838152 + -0.5 = -43.85838152 x = -43.85838152 Simplifying x = -43.85838152Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.85838152, -43.85838152}
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