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Simplifying x2 + 8x + -221 = 0 Reorder the terms: -221 + 8x + x2 = 0 Solving -221 + 8x + 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 + 8x + 221 + x2 = 0 + 221 Reorder the terms: -221 + 221 + 8x + x2 = 0 + 221 Combine like terms: -221 + 221 = 0 0 + 8x + x2 = 0 + 221 8x + x2 = 0 + 221 Combine like terms: 0 + 221 = 221 8x + x2 = 221 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 = 221 + 16 Reorder the terms: 16 + 8x + x2 = 221 + 16 Combine like terms: 221 + 16 = 237 16 + 8x + x2 = 237 Factor a perfect square on the left side: (x + 4)(x + 4) = 237 Calculate the square root of the right side: 15.394804318 Break this problem into two subproblems by setting (x + 4) equal to 15.394804318 and -15.394804318.Subproblem 1
x + 4 = 15.394804318 Simplifying x + 4 = 15.394804318 Reorder the terms: 4 + x = 15.394804318 Solving 4 + x = 15.394804318 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 = 15.394804318 + -4 Combine like terms: 4 + -4 = 0 0 + x = 15.394804318 + -4 x = 15.394804318 + -4 Combine like terms: 15.394804318 + -4 = 11.394804318 x = 11.394804318 Simplifying x = 11.394804318Subproblem 2
x + 4 = -15.394804318 Simplifying x + 4 = -15.394804318 Reorder the terms: 4 + x = -15.394804318 Solving 4 + x = -15.394804318 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 = -15.394804318 + -4 Combine like terms: 4 + -4 = 0 0 + x = -15.394804318 + -4 x = -15.394804318 + -4 Combine like terms: -15.394804318 + -4 = -19.394804318 x = -19.394804318 Simplifying x = -19.394804318Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.394804318, -19.394804318}
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