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Simplifying x2 + 8x + -211 = 0 Reorder the terms: -211 + 8x + x2 = 0 Solving -211 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '211' to each side of the equation. -211 + 8x + 211 + x2 = 0 + 211 Reorder the terms: -211 + 211 + 8x + x2 = 0 + 211 Combine like terms: -211 + 211 = 0 0 + 8x + x2 = 0 + 211 8x + x2 = 0 + 211 Combine like terms: 0 + 211 = 211 8x + x2 = 211 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 211 + 16 Reorder the terms: 16 + 8x + x2 = 211 + 16 Combine like terms: 211 + 16 = 227 16 + 8x + x2 = 227 Factor a perfect square on the left side: (x + 4)(x + 4) = 227 Calculate the square root of the right side: 15.066519173 Break this problem into two subproblems by setting (x + 4) equal to 15.066519173 and -15.066519173.Subproblem 1
x + 4 = 15.066519173 Simplifying x + 4 = 15.066519173 Reorder the terms: 4 + x = 15.066519173 Solving 4 + x = 15.066519173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 15.066519173 + -4 Combine like terms: 4 + -4 = 0 0 + x = 15.066519173 + -4 x = 15.066519173 + -4 Combine like terms: 15.066519173 + -4 = 11.066519173 x = 11.066519173 Simplifying x = 11.066519173Subproblem 2
x + 4 = -15.066519173 Simplifying x + 4 = -15.066519173 Reorder the terms: 4 + x = -15.066519173 Solving 4 + x = -15.066519173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -15.066519173 + -4 Combine like terms: 4 + -4 = 0 0 + x = -15.066519173 + -4 x = -15.066519173 + -4 Combine like terms: -15.066519173 + -4 = -19.066519173 x = -19.066519173 Simplifying x = -19.066519173Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.066519173, -19.066519173}
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