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Simplifying (x2 + 2x + -221) = 0 Reorder the terms: (-221 + 2x + x2) = 0 Remove parenthesis around (-221 + 2x + x2) -221 + 2x + x2 = 0 Solving -221 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '221' to each side of the equation. -221 + 2x + 221 + x2 = 0 + 221 Reorder the terms: -221 + 221 + 2x + x2 = 0 + 221 Combine like terms: -221 + 221 = 0 0 + 2x + x2 = 0 + 221 2x + x2 = 0 + 221 Combine like terms: 0 + 221 = 221 2x + x2 = 221 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 = 221 + 1 Reorder the terms: 1 + 2x + x2 = 221 + 1 Combine like terms: 221 + 1 = 222 1 + 2x + x2 = 222 Factor a perfect square on the left side: (x + 1)(x + 1) = 222 Calculate the square root of the right side: 14.899664426 Break this problem into two subproblems by setting (x + 1) equal to 14.899664426 and -14.899664426.Subproblem 1
x + 1 = 14.899664426 Simplifying x + 1 = 14.899664426 Reorder the terms: 1 + x = 14.899664426 Solving 1 + x = 14.899664426 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 = 14.899664426 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.899664426 + -1 x = 14.899664426 + -1 Combine like terms: 14.899664426 + -1 = 13.899664426 x = 13.899664426 Simplifying x = 13.899664426Subproblem 2
x + 1 = -14.899664426 Simplifying x + 1 = -14.899664426 Reorder the terms: 1 + x = -14.899664426 Solving 1 + x = -14.899664426 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 = -14.899664426 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.899664426 + -1 x = -14.899664426 + -1 Combine like terms: -14.899664426 + -1 = -15.899664426 x = -15.899664426 Simplifying x = -15.899664426Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.899664426, -15.899664426}
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