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Simplifying x(x + 2) = 220 Reorder the terms: x(2 + x) = 220 (2 * x + x * x) = 220 (2x + x2) = 220 Solving 2x + x2 = 220 Solving for variable 'x'. Reorder the terms: -220 + 2x + x2 = 220 + -220 Combine like terms: 220 + -220 = 0 -220 + 2x + x2 = 0 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 = 13.866068747 x = 13.866068747 Simplifying x = 13.866068747Subproblem 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 = -15.866068747 x = -15.866068747 Simplifying x = -15.866068747Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.866068747, -15.866068747}
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