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Simplifying x4 + x2 + -396 = 0 Reorder the terms: -396 + x2 + x4 = 0 Solving -396 + x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '396' to each side of the equation. -396 + x2 + 396 + x4 = 0 + 396 Reorder the terms: -396 + 396 + x2 + x4 = 0 + 396 Combine like terms: -396 + 396 = 0 0 + x2 + x4 = 0 + 396 x2 + x4 = 0 + 396 Combine like terms: 0 + 396 = 396 x2 + x4 = 396 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x2 + 0.25 + x4 = 396 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 396 + 0.25 Combine like terms: 396 + 0.25 = 396.25 0.25 + x2 + x4 = 396.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 396.25 Calculate the square root of the right side: 19.906029237 Break this problem into two subproblems by setting (x2 + 0.5) equal to 19.906029237 and -19.906029237.Subproblem 1
x2 + 0.5 = 19.906029237 Simplifying x2 + 0.5 = 19.906029237 Reorder the terms: 0.5 + x2 = 19.906029237 Solving 0.5 + x2 = 19.906029237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 19.906029237 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 19.906029237 + -0.5 x2 = 19.906029237 + -0.5 Combine like terms: 19.906029237 + -0.5 = 19.406029237 x2 = 19.406029237 Simplifying x2 = 19.406029237 Take the square root of each side: x = {-4.40522749, 4.40522749}Subproblem 2
x2 + 0.5 = -19.906029237 Simplifying x2 + 0.5 = -19.906029237 Reorder the terms: 0.5 + x2 = -19.906029237 Solving 0.5 + x2 = -19.906029237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -19.906029237 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -19.906029237 + -0.5 x2 = -19.906029237 + -0.5 Combine like terms: -19.906029237 + -0.5 = -20.406029237 x2 = -20.406029237 Simplifying x2 = -20.406029237 Reorder the terms: 20.406029237 + x2 = -20.406029237 + 20.406029237 Combine like terms: -20.406029237 + 20.406029237 = 0.000000000 20.406029237 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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