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Simplifying [x(x + 8)] + -256 = 0 Reorder the terms: [x(8 + x)] + -256 = 0 [(8 * x + x * x)] + -256 = 0 [(8x + x2)] + -256 = 0 [8x + x2] + -256 = 0 Remove brackets around [8x + x2] 8x + x2 + -256 = 0 Reorder the terms: -256 + 8x + x2 = 0 Solving -256 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + 8x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 8x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 8x + x2 = 0 + 256 8x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 8x + x2 = 256 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 = 256 + 16 Reorder the terms: 16 + 8x + x2 = 256 + 16 Combine like terms: 256 + 16 = 272 16 + 8x + x2 = 272 Factor a perfect square on the left side: (x + 4)(x + 4) = 272 Calculate the square root of the right side: 16.492422502 Break this problem into two subproblems by setting (x + 4) equal to 16.492422502 and -16.492422502.Subproblem 1
x + 4 = 16.492422502 Simplifying x + 4 = 16.492422502 Reorder the terms: 4 + x = 16.492422502 Solving 4 + x = 16.492422502 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 = 16.492422502 + -4 Combine like terms: 4 + -4 = 0 0 + x = 16.492422502 + -4 x = 16.492422502 + -4 Combine like terms: 16.492422502 + -4 = 12.492422502 x = 12.492422502 Simplifying x = 12.492422502Subproblem 2
x + 4 = -16.492422502 Simplifying x + 4 = -16.492422502 Reorder the terms: 4 + x = -16.492422502 Solving 4 + x = -16.492422502 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 = -16.492422502 + -4 Combine like terms: 4 + -4 = 0 0 + x = -16.492422502 + -4 x = -16.492422502 + -4 Combine like terms: -16.492422502 + -4 = -20.492422502 x = -20.492422502 Simplifying x = -20.492422502Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.492422502, -20.492422502}
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