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Simplifying X2 + 22X + 1 = 0 Reorder the terms: 1 + 22X + X2 = 0 Solving 1 + 22X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 22X + -1 + X2 = 0 + -1 Reorder the terms: 1 + -1 + 22X + X2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 22X + X2 = 0 + -1 22X + X2 = 0 + -1 Combine like terms: 0 + -1 = -1 22X + X2 = -1 The X term is 22X. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22X + 121 + X2 = -1 + 121 Reorder the terms: 121 + 22X + X2 = -1 + 121 Combine like terms: -1 + 121 = 120 121 + 22X + X2 = 120 Factor a perfect square on the left side: (X + 11)(X + 11) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (X + 11) equal to 10.95445115 and -10.95445115.Subproblem 1
X + 11 = 10.95445115 Simplifying X + 11 = 10.95445115 Reorder the terms: 11 + X = 10.95445115 Solving 11 + X = 10.95445115 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + X = 10.95445115 + -11 Combine like terms: 11 + -11 = 0 0 + X = 10.95445115 + -11 X = 10.95445115 + -11 Combine like terms: 10.95445115 + -11 = -0.04554885 X = -0.04554885 Simplifying X = -0.04554885Subproblem 2
X + 11 = -10.95445115 Simplifying X + 11 = -10.95445115 Reorder the terms: 11 + X = -10.95445115 Solving 11 + X = -10.95445115 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + X = -10.95445115 + -11 Combine like terms: 11 + -11 = 0 0 + X = -10.95445115 + -11 X = -10.95445115 + -11 Combine like terms: -10.95445115 + -11 = -21.95445115 X = -21.95445115 Simplifying X = -21.95445115Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.04554885, -21.95445115}
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