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Simplifying x2 + -24x + -128 = 0 Reorder the terms: -128 + -24x + x2 = 0 Solving -128 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + -24x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + -24x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + -24x + x2 = 0 + 128 -24x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 -24x + x2 = 128 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 128 + 144 Reorder the terms: 144 + -24x + x2 = 128 + 144 Combine like terms: 128 + 144 = 272 144 + -24x + x2 = 272 Factor a perfect square on the left side: (x + -12)(x + -12) = 272 Calculate the square root of the right side: 16.492422502 Break this problem into two subproblems by setting (x + -12) equal to 16.492422502 and -16.492422502.Subproblem 1
x + -12 = 16.492422502 Simplifying x + -12 = 16.492422502 Reorder the terms: -12 + x = 16.492422502 Solving -12 + x = 16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 16.492422502 + 12 Combine like terms: -12 + 12 = 0 0 + x = 16.492422502 + 12 x = 16.492422502 + 12 Combine like terms: 16.492422502 + 12 = 28.492422502 x = 28.492422502 Simplifying x = 28.492422502Subproblem 2
x + -12 = -16.492422502 Simplifying x + -12 = -16.492422502 Reorder the terms: -12 + x = -16.492422502 Solving -12 + x = -16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -16.492422502 + 12 Combine like terms: -12 + 12 = 0 0 + x = -16.492422502 + 12 x = -16.492422502 + 12 Combine like terms: -16.492422502 + 12 = -4.492422502 x = -4.492422502 Simplifying x = -4.492422502Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.492422502, -4.492422502}
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