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Simplifying x2 + 2x + -2162 = 0 Reorder the terms: -2162 + 2x + x2 = 0 Solving -2162 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2162' to each side of the equation. -2162 + 2x + 2162 + x2 = 0 + 2162 Reorder the terms: -2162 + 2162 + 2x + x2 = 0 + 2162 Combine like terms: -2162 + 2162 = 0 0 + 2x + x2 = 0 + 2162 2x + x2 = 0 + 2162 Combine like terms: 0 + 2162 = 2162 2x + x2 = 2162 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 2162 + 1 Reorder the terms: 1 + 2x + x2 = 2162 + 1 Combine like terms: 2162 + 1 = 2163 1 + 2x + x2 = 2163 Factor a perfect square on the left side: (x + 1)(x + 1) = 2163 Calculate the square root of the right side: 46.508063817 Break this problem into two subproblems by setting (x + 1) equal to 46.508063817 and -46.508063817.Subproblem 1
x + 1 = 46.508063817 Simplifying x + 1 = 46.508063817 Reorder the terms: 1 + x = 46.508063817 Solving 1 + x = 46.508063817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 46.508063817 + -1 Combine like terms: 1 + -1 = 0 0 + x = 46.508063817 + -1 x = 46.508063817 + -1 Combine like terms: 46.508063817 + -1 = 45.508063817 x = 45.508063817 Simplifying x = 45.508063817Subproblem 2
x + 1 = -46.508063817 Simplifying x + 1 = -46.508063817 Reorder the terms: 1 + x = -46.508063817 Solving 1 + x = -46.508063817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -46.508063817 + -1 Combine like terms: 1 + -1 = 0 0 + x = -46.508063817 + -1 x = -46.508063817 + -1 Combine like terms: -46.508063817 + -1 = -47.508063817 x = -47.508063817 Simplifying x = -47.508063817Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.508063817, -47.508063817}
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