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Simplifying x2 + -40x + 5 = 0 Reorder the terms: 5 + -40x + x2 = 0 Solving 5 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -40x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -40x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -40x + x2 = 0 + -5 -40x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -40x + x2 = -5 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -5 + 400 Reorder the terms: 400 + -40x + x2 = -5 + 400 Combine like terms: -5 + 400 = 395 400 + -40x + x2 = 395 Factor a perfect square on the left side: (x + -20)(x + -20) = 395 Calculate the square root of the right side: 19.874606914 Break this problem into two subproblems by setting (x + -20) equal to 19.874606914 and -19.874606914.Subproblem 1
x + -20 = 19.874606914 Simplifying x + -20 = 19.874606914 Reorder the terms: -20 + x = 19.874606914 Solving -20 + x = 19.874606914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 19.874606914 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.874606914 + 20 x = 19.874606914 + 20 Combine like terms: 19.874606914 + 20 = 39.874606914 x = 39.874606914 Simplifying x = 39.874606914Subproblem 2
x + -20 = -19.874606914 Simplifying x + -20 = -19.874606914 Reorder the terms: -20 + x = -19.874606914 Solving -20 + x = -19.874606914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -19.874606914 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.874606914 + 20 x = -19.874606914 + 20 Combine like terms: -19.874606914 + 20 = 0.125393086 x = 0.125393086 Simplifying x = 0.125393086Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.874606914, 0.125393086}
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