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Simplifying x2 + -8x + -255 = 0 Reorder the terms: -255 + -8x + x2 = 0 Solving -255 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '255' to each side of the equation. -255 + -8x + 255 + x2 = 0 + 255 Reorder the terms: -255 + 255 + -8x + x2 = 0 + 255 Combine like terms: -255 + 255 = 0 0 + -8x + x2 = 0 + 255 -8x + x2 = 0 + 255 Combine like terms: 0 + 255 = 255 -8x + x2 = 255 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 = 255 + 16 Reorder the terms: 16 + -8x + x2 = 255 + 16 Combine like terms: 255 + 16 = 271 16 + -8x + x2 = 271 Factor a perfect square on the left side: (x + -4)(x + -4) = 271 Calculate the square root of the right side: 16.462077633 Break this problem into two subproblems by setting (x + -4) equal to 16.462077633 and -16.462077633.Subproblem 1
x + -4 = 16.462077633 Simplifying x + -4 = 16.462077633 Reorder the terms: -4 + x = 16.462077633 Solving -4 + x = 16.462077633 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 = 16.462077633 + 4 Combine like terms: -4 + 4 = 0 0 + x = 16.462077633 + 4 x = 16.462077633 + 4 Combine like terms: 16.462077633 + 4 = 20.462077633 x = 20.462077633 Simplifying x = 20.462077633Subproblem 2
x + -4 = -16.462077633 Simplifying x + -4 = -16.462077633 Reorder the terms: -4 + x = -16.462077633 Solving -4 + x = -16.462077633 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 = -16.462077633 + 4 Combine like terms: -4 + 4 = 0 0 + x = -16.462077633 + 4 x = -16.462077633 + 4 Combine like terms: -16.462077633 + 4 = -12.462077633 x = -12.462077633 Simplifying x = -12.462077633Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.462077633, -12.462077633}
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