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Simplifying -32x = 16 + -1x2 Solving -32x = 16 + -1x2 Solving for variable 'x'. Reorder the terms: -16 + -32x + x2 = 16 + -1x2 + -16 + x2 Reorder the terms: -16 + -32x + x2 = 16 + -16 + -1x2 + x2 Combine like terms: 16 + -16 = 0 -16 + -32x + x2 = 0 + -1x2 + x2 -16 + -32x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -16 + -32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -32x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -32x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -32x + x2 = 0 + 16 -32x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -32x + x2 = 16 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = 16 + 256 Reorder the terms: 256 + -32x + x2 = 16 + 256 Combine like terms: 16 + 256 = 272 256 + -32x + x2 = 272 Factor a perfect square on the left side: (x + -16)(x + -16) = 272 Calculate the square root of the right side: 16.492422502 Break this problem into two subproblems by setting (x + -16) equal to 16.492422502 and -16.492422502.Subproblem 1
x + -16 = 16.492422502 Simplifying x + -16 = 16.492422502 Reorder the terms: -16 + x = 16.492422502 Solving -16 + x = 16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 16.492422502 + 16 Combine like terms: -16 + 16 = 0 0 + x = 16.492422502 + 16 x = 16.492422502 + 16 Combine like terms: 16.492422502 + 16 = 32.492422502 x = 32.492422502 Simplifying x = 32.492422502Subproblem 2
x + -16 = -16.492422502 Simplifying x + -16 = -16.492422502 Reorder the terms: -16 + x = -16.492422502 Solving -16 + x = -16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -16.492422502 + 16 Combine like terms: -16 + 16 = 0 0 + x = -16.492422502 + 16 x = -16.492422502 + 16 Combine like terms: -16.492422502 + 16 = -0.492422502 x = -0.492422502 Simplifying x = -0.492422502Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.492422502, -0.492422502}
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