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Simplifying x + x2 = 2.2222222 Solving x + x2 = 2.2222222 Solving for variable 'x'. Reorder the terms: -2.2222222 + x + x2 = 2.2222222 + -2.2222222 Combine like terms: 2.2222222 + -2.2222222 = 0.0000000 -2.2222222 + x + x2 = 0.0000000 Begin completing the square. Move the constant term to the right: Add '2.2222222' to each side of the equation. -2.2222222 + x + 2.2222222 + x2 = 0.0000000 + 2.2222222 Reorder the terms: -2.2222222 + 2.2222222 + x + x2 = 0.0000000 + 2.2222222 Combine like terms: -2.2222222 + 2.2222222 = 0.0000000 0.0000000 + x + x2 = 0.0000000 + 2.2222222 x + x2 = 0.0000000 + 2.2222222 Combine like terms: 0.0000000 + 2.2222222 = 2.2222222 x + x2 = 2.2222222 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 2.2222222 + 0.25 Reorder the terms: 0.25 + x + x2 = 2.2222222 + 0.25 Combine like terms: 2.2222222 + 0.25 = 2.4722222 0.25 + x + x2 = 2.4722222 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.4722222 Calculate the square root of the right side: 1.572330182 Break this problem into two subproblems by setting (x + 0.5) equal to 1.572330182 and -1.572330182.Subproblem 1
x + 0.5 = 1.572330182 Simplifying x + 0.5 = 1.572330182 Reorder the terms: 0.5 + x = 1.572330182 Solving 0.5 + x = 1.572330182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.572330182 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.572330182 + -0.5 x = 1.572330182 + -0.5 Combine like terms: 1.572330182 + -0.5 = 1.072330182 x = 1.072330182 Simplifying x = 1.072330182Subproblem 2
x + 0.5 = -1.572330182 Simplifying x + 0.5 = -1.572330182 Reorder the terms: 0.5 + x = -1.572330182 Solving 0.5 + x = -1.572330182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.572330182 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.572330182 + -0.5 x = -1.572330182 + -0.5 Combine like terms: -1.572330182 + -0.5 = -2.072330182 x = -2.072330182 Simplifying x = -2.072330182Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.072330182, -2.072330182}
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