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Simplifying x2 + 2x + -505 = 0 Reorder the terms: -505 + 2x + x2 = 0 Solving -505 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '505' to each side of the equation. -505 + 2x + 505 + x2 = 0 + 505 Reorder the terms: -505 + 505 + 2x + x2 = 0 + 505 Combine like terms: -505 + 505 = 0 0 + 2x + x2 = 0 + 505 2x + x2 = 0 + 505 Combine like terms: 0 + 505 = 505 2x + x2 = 505 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 = 505 + 1 Reorder the terms: 1 + 2x + x2 = 505 + 1 Combine like terms: 505 + 1 = 506 1 + 2x + x2 = 506 Factor a perfect square on the left side: (x + 1)(x + 1) = 506 Calculate the square root of the right side: 22.494443758 Break this problem into two subproblems by setting (x + 1) equal to 22.494443758 and -22.494443758.Subproblem 1
x + 1 = 22.494443758 Simplifying x + 1 = 22.494443758 Reorder the terms: 1 + x = 22.494443758 Solving 1 + x = 22.494443758 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 = 22.494443758 + -1 Combine like terms: 1 + -1 = 0 0 + x = 22.494443758 + -1 x = 22.494443758 + -1 Combine like terms: 22.494443758 + -1 = 21.494443758 x = 21.494443758 Simplifying x = 21.494443758Subproblem 2
x + 1 = -22.494443758 Simplifying x + 1 = -22.494443758 Reorder the terms: 1 + x = -22.494443758 Solving 1 + x = -22.494443758 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 = -22.494443758 + -1 Combine like terms: 1 + -1 = 0 0 + x = -22.494443758 + -1 x = -22.494443758 + -1 Combine like terms: -22.494443758 + -1 = -23.494443758 x = -23.494443758 Simplifying x = -23.494443758Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.494443758, -23.494443758}
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