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Simplifying x2 + x = 2208 Reorder the terms: x + x2 = 2208 Solving x + x2 = 2208 Solving for variable 'x'. Reorder the terms: -2208 + x + x2 = 2208 + -2208 Combine like terms: 2208 + -2208 = 0 -2208 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2208' to each side of the equation. -2208 + x + 2208 + x2 = 0 + 2208 Reorder the terms: -2208 + 2208 + x + x2 = 0 + 2208 Combine like terms: -2208 + 2208 = 0 0 + x + x2 = 0 + 2208 x + x2 = 0 + 2208 Combine like terms: 0 + 2208 = 2208 x + x2 = 2208 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 = 2208 + 0.25 Reorder the terms: 0.25 + x + x2 = 2208 + 0.25 Combine like terms: 2208 + 0.25 = 2208.25 0.25 + x + x2 = 2208.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2208.25 Calculate the square root of the right side: 46.992020599 Break this problem into two subproblems by setting (x + 0.5) equal to 46.992020599 and -46.992020599.Subproblem 1
x + 0.5 = 46.992020599 Simplifying x + 0.5 = 46.992020599 Reorder the terms: 0.5 + x = 46.992020599 Solving 0.5 + x = 46.992020599 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 = 46.992020599 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 46.992020599 + -0.5 x = 46.992020599 + -0.5 Combine like terms: 46.992020599 + -0.5 = 46.492020599 x = 46.492020599 Simplifying x = 46.492020599Subproblem 2
x + 0.5 = -46.992020599 Simplifying x + 0.5 = -46.992020599 Reorder the terms: 0.5 + x = -46.992020599 Solving 0.5 + x = -46.992020599 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 = -46.992020599 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -46.992020599 + -0.5 x = -46.992020599 + -0.5 Combine like terms: -46.992020599 + -0.5 = -47.492020599 x = -47.492020599 Simplifying x = -47.492020599Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.492020599, -47.492020599}
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