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Simplifying x2 + 40x + 11 = 0 Reorder the terms: 11 + 40x + x2 = 0 Solving 11 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 40x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 40x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 40x + x2 = 0 + -11 40x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 40x + x2 = -11 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 = -11 + 400 Reorder the terms: 400 + 40x + x2 = -11 + 400 Combine like terms: -11 + 400 = 389 400 + 40x + x2 = 389 Factor a perfect square on the left side: (x + 20)(x + 20) = 389 Calculate the square root of the right side: 19.723082923 Break this problem into two subproblems by setting (x + 20) equal to 19.723082923 and -19.723082923.Subproblem 1
x + 20 = 19.723082923 Simplifying x + 20 = 19.723082923 Reorder the terms: 20 + x = 19.723082923 Solving 20 + x = 19.723082923 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 = 19.723082923 + -20 Combine like terms: 20 + -20 = 0 0 + x = 19.723082923 + -20 x = 19.723082923 + -20 Combine like terms: 19.723082923 + -20 = -0.276917077 x = -0.276917077 Simplifying x = -0.276917077Subproblem 2
x + 20 = -19.723082923 Simplifying x + 20 = -19.723082923 Reorder the terms: 20 + x = -19.723082923 Solving 20 + x = -19.723082923 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 = -19.723082923 + -20 Combine like terms: 20 + -20 = 0 0 + x = -19.723082923 + -20 x = -19.723082923 + -20 Combine like terms: -19.723082923 + -20 = -39.723082923 x = -39.723082923 Simplifying x = -39.723082923Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.276917077, -39.723082923}
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