X^4-50X^2-49=0

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Solution for X^4-50X^2-49=0 equation:


Simplifying
X4 + -50X2 + -49 = 0

Reorder the terms:
-49 + -50X2 + X4 = 0

Solving
-49 + -50X2 + X4 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -50X2 + 49 + X4 = 0 + 49

Reorder the terms:
-49 + 49 + -50X2 + X4 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -50X2 + X4 = 0 + 49
-50X2 + X4 = 0 + 49

Combine like terms: 0 + 49 = 49
-50X2 + X4 = 49

The X term is -50X2.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50X2 + 625 + X4 = 49 + 625

Reorder the terms:
625 + -50X2 + X4 = 49 + 625

Combine like terms: 49 + 625 = 674
625 + -50X2 + X4 = 674

Factor a perfect square on the left side:
(X2 + -25)(X2 + -25) = 674

Calculate the square root of the right side: 25.961509971

Break this problem into two subproblems by setting 
(X2 + -25) equal to 25.961509971 and -25.961509971.

Subproblem 1

X2 + -25 = 25.961509971 Simplifying X2 + -25 = 25.961509971 Reorder the terms: -25 + X2 = 25.961509971 Solving -25 + X2 = 25.961509971 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + X2 = 25.961509971 + 25 Combine like terms: -25 + 25 = 0 0 + X2 = 25.961509971 + 25 X2 = 25.961509971 + 25 Combine like terms: 25.961509971 + 25 = 50.961509971 X2 = 50.961509971 Simplifying X2 = 50.961509971 Take the square root of each side: X = {-7.138733079, 7.138733079}

Subproblem 2

X2 + -25 = -25.961509971 Simplifying X2 + -25 = -25.961509971 Reorder the terms: -25 + X2 = -25.961509971 Solving -25 + X2 = -25.961509971 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + X2 = -25.961509971 + 25 Combine like terms: -25 + 25 = 0 0 + X2 = -25.961509971 + 25 X2 = -25.961509971 + 25 Combine like terms: -25.961509971 + 25 = -0.961509971 X2 = -0.961509971 Simplifying X2 = -0.961509971 Reorder the terms: 0.961509971 + X2 = -0.961509971 + 0.961509971 Combine like terms: -0.961509971 + 0.961509971 = 0.000000000 0.961509971 + 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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