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Simplifying x2 + 21x + 41 = 0 Reorder the terms: 41 + 21x + x2 = 0 Solving 41 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 21x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + 21x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 21x + x2 = 0 + -41 21x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 21x + x2 = -41 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = -41 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -41 + 110.25 Combine like terms: -41 + 110.25 = 69.25 110.25 + 21x + x2 = 69.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + 10.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + 10.5 = 8.321658489 Simplifying x + 10.5 = 8.321658489 Reorder the terms: 10.5 + x = 8.321658489 Solving 10.5 + x = 8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 8.321658489 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 8.321658489 + -10.5 x = 8.321658489 + -10.5 Combine like terms: 8.321658489 + -10.5 = -2.178341511 x = -2.178341511 Simplifying x = -2.178341511Subproblem 2
x + 10.5 = -8.321658489 Simplifying x + 10.5 = -8.321658489 Reorder the terms: 10.5 + x = -8.321658489 Solving 10.5 + x = -8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -8.321658489 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -8.321658489 + -10.5 x = -8.321658489 + -10.5 Combine like terms: -8.321658489 + -10.5 = -18.821658489 x = -18.821658489 Simplifying x = -18.821658489Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.178341511, -18.821658489}
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