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Simplifying x2 + 2x + -205 = 0 Reorder the terms: -205 + 2x + x2 = 0 Solving -205 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '205' to each side of the equation. -205 + 2x + 205 + x2 = 0 + 205 Reorder the terms: -205 + 205 + 2x + x2 = 0 + 205 Combine like terms: -205 + 205 = 0 0 + 2x + x2 = 0 + 205 2x + x2 = 0 + 205 Combine like terms: 0 + 205 = 205 2x + x2 = 205 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 = 205 + 1 Reorder the terms: 1 + 2x + x2 = 205 + 1 Combine like terms: 205 + 1 = 206 1 + 2x + x2 = 206 Factor a perfect square on the left side: (x + 1)(x + 1) = 206 Calculate the square root of the right side: 14.352700094 Break this problem into two subproblems by setting (x + 1) equal to 14.352700094 and -14.352700094.Subproblem 1
x + 1 = 14.352700094 Simplifying x + 1 = 14.352700094 Reorder the terms: 1 + x = 14.352700094 Solving 1 + x = 14.352700094 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 = 14.352700094 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.352700094 + -1 x = 14.352700094 + -1 Combine like terms: 14.352700094 + -1 = 13.352700094 x = 13.352700094 Simplifying x = 13.352700094Subproblem 2
x + 1 = -14.352700094 Simplifying x + 1 = -14.352700094 Reorder the terms: 1 + x = -14.352700094 Solving 1 + x = -14.352700094 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 = -14.352700094 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.352700094 + -1 x = -14.352700094 + -1 Combine like terms: -14.352700094 + -1 = -15.352700094 x = -15.352700094 Simplifying x = -15.352700094Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.352700094, -15.352700094}
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