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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 = -0.125393086 x = -0.125393086 Simplifying x = -0.125393086Subproblem 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 = -39.874606914 x = -39.874606914 Simplifying x = -39.874606914Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.125393086, -39.874606914}
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