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Simplifying x2 + -2x + -220 = 0 Reorder the terms: -220 + -2x + x2 = 0 Solving -220 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '220' to each side of the equation. -220 + -2x + 220 + x2 = 0 + 220 Reorder the terms: -220 + 220 + -2x + x2 = 0 + 220 Combine like terms: -220 + 220 = 0 0 + -2x + x2 = 0 + 220 -2x + x2 = 0 + 220 Combine like terms: 0 + 220 = 220 -2x + x2 = 220 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 = 220 + 1 Reorder the terms: 1 + -2x + x2 = 220 + 1 Combine like terms: 220 + 1 = 221 1 + -2x + x2 = 221 Factor a perfect square on the left side: (x + -1)(x + -1) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (x + -1) equal to 14.866068747 and -14.866068747.Subproblem 1
x + -1 = 14.866068747 Simplifying x + -1 = 14.866068747 Reorder the terms: -1 + x = 14.866068747 Solving -1 + x = 14.866068747 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 = 14.866068747 + 1 Combine like terms: -1 + 1 = 0 0 + x = 14.866068747 + 1 x = 14.866068747 + 1 Combine like terms: 14.866068747 + 1 = 15.866068747 x = 15.866068747 Simplifying x = 15.866068747Subproblem 2
x + -1 = -14.866068747 Simplifying x + -1 = -14.866068747 Reorder the terms: -1 + x = -14.866068747 Solving -1 + x = -14.866068747 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 = -14.866068747 + 1 Combine like terms: -1 + 1 = 0 0 + x = -14.866068747 + 1 x = -14.866068747 + 1 Combine like terms: -14.866068747 + 1 = -13.866068747 x = -13.866068747 Simplifying x = -13.866068747Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.866068747, -13.866068747}
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