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Simplifying x2 + 2x + -843 = 0 Reorder the terms: -843 + 2x + x2 = 0 Solving -843 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '843' to each side of the equation. -843 + 2x + 843 + x2 = 0 + 843 Reorder the terms: -843 + 843 + 2x + x2 = 0 + 843 Combine like terms: -843 + 843 = 0 0 + 2x + x2 = 0 + 843 2x + x2 = 0 + 843 Combine like terms: 0 + 843 = 843 2x + x2 = 843 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 = 843 + 1 Reorder the terms: 1 + 2x + x2 = 843 + 1 Combine like terms: 843 + 1 = 844 1 + 2x + x2 = 844 Factor a perfect square on the left side: (x + 1)(x + 1) = 844 Calculate the square root of the right side: 29.051678093 Break this problem into two subproblems by setting (x + 1) equal to 29.051678093 and -29.051678093.Subproblem 1
x + 1 = 29.051678093 Simplifying x + 1 = 29.051678093 Reorder the terms: 1 + x = 29.051678093 Solving 1 + x = 29.051678093 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 = 29.051678093 + -1 Combine like terms: 1 + -1 = 0 0 + x = 29.051678093 + -1 x = 29.051678093 + -1 Combine like terms: 29.051678093 + -1 = 28.051678093 x = 28.051678093 Simplifying x = 28.051678093Subproblem 2
x + 1 = -29.051678093 Simplifying x + 1 = -29.051678093 Reorder the terms: 1 + x = -29.051678093 Solving 1 + x = -29.051678093 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 = -29.051678093 + -1 Combine like terms: 1 + -1 = 0 0 + x = -29.051678093 + -1 x = -29.051678093 + -1 Combine like terms: -29.051678093 + -1 = -30.051678093 x = -30.051678093 Simplifying x = -30.051678093Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.051678093, -30.051678093}
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