x^4-49x^2-360=0

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Solution for x^4-49x^2-360=0 equation: 


Simplifying
x4 + -49x2 + -360 = 0

Reorder the terms:
-360 + -49x2 + x4 = 0

Solving
-360 + -49x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '360' to each side of the equation.
-360 + -49x2 + 360 + x4 = 0 + 360

Reorder the terms:
-360 + 360 + -49x2 + x4 = 0 + 360

Combine like terms: -360 + 360 = 0
0 + -49x2 + x4 = 0 + 360
-49x2 + x4 = 0 + 360

Combine like terms: 0 + 360 = 360
-49x2 + x4 = 360

The x term is -49x2.  Take half its coefficient (-24.5).
Square it (600.25) and add it to both sides.

Add '600.25' to each side of the equation.
-49x2 + 600.25 + x4 = 360 + 600.25

Reorder the terms:
600.25 + -49x2 + x4 = 360 + 600.25

Combine like terms: 360 + 600.25 = 960.25
600.25 + -49x2 + x4 = 960.25

Factor a perfect square on the left side:
(x2 + -24.5)(x2 + -24.5) = 960.25

Calculate the square root of the right side: 30.987900865

Break this problem into two subproblems by setting 
(x2 + -24.5) equal to 30.987900865 and -30.987900865.


Subproblem 1
x2 + -24.5 = 30.987900865

Simplifying
x2 + -24.5 = 30.987900865

Reorder the terms:
-24.5 + x2 = 30.987900865

Solving
-24.5 + x2 = 30.987900865

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '24.5' to each side of the equation.
-24.5 + 24.5 + x2 = 30.987900865 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + x2 = 30.987900865 + 24.5
x2 = 30.987900865 + 24.5

Combine like terms: 30.987900865 + 24.5 = 55.487900865
x2 = 55.487900865

Simplifying
x2 = 55.487900865

Take the square root of each side:
x = {-7.449020128, 7.449020128}


Subproblem 2
x2 + -24.5 = -30.987900865

Simplifying
x2 + -24.5 = -30.987900865

Reorder the terms:
-24.5 + x2 = -30.987900865

Solving
-24.5 + x2 = -30.987900865

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '24.5' to each side of the equation.
-24.5 + 24.5 + x2 = -30.987900865 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + x2 = -30.987900865 + 24.5
x2 = -30.987900865 + 24.5

Combine like terms: -30.987900865 + 24.5 = -6.487900865
x2 = -6.487900865

Simplifying
x2 = -6.487900865

Reorder the terms:
6.487900865 + x2 = -6.487900865 + 6.487900865

Combine like terms: -6.487900865 + 6.487900865 = 0.000000000
6.487900865 + 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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