x^4-5x^2+4=48

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Solution for x^4-5x^2+4=48 equation: 


Simplifying
x4 + -5x2 + 4 = 48

Reorder the terms:
4 + -5x2 + x4 = 48

Solving
4 + -5x2 + x4 = 48

Solving for variable 'x'.

Reorder the terms:
4 + -48 + -5x2 + x4 = 48 + -48

Combine like terms: 4 + -48 = -44
-44 + -5x2 + x4 = 48 + -48

Combine like terms: 48 + -48 = 0
-44 + -5x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -5x2 + 44 + x4 = 0 + 44

Reorder the terms:
-44 + 44 + -5x2 + x4 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -5x2 + x4 = 0 + 44
-5x2 + x4 = 0 + 44

Combine like terms: 0 + 44 = 44
-5x2 + x4 = 44

The x term is -5x2.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x2 + 6.25 + x4 = 44 + 6.25

Reorder the terms:
6.25 + -5x2 + x4 = 44 + 6.25

Combine like terms: 44 + 6.25 = 50.25
6.25 + -5x2 + x4 = 50.25

Factor a perfect square on the left side:
(x2 + -2.5)(x2 + -2.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(x2 + -2.5) equal to 7.088723439 and -7.088723439.


Subproblem 1
x2 + -2.5 = 7.088723439

Simplifying
x2 + -2.5 = 7.088723439

Reorder the terms:
-2.5 + x2 = 7.088723439

Solving
-2.5 + x2 = 7.088723439

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x2 = 7.088723439 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x2 = 7.088723439 + 2.5
x2 = 7.088723439 + 2.5

Combine like terms: 7.088723439 + 2.5 = 9.588723439
x2 = 9.588723439

Simplifying
x2 = 9.588723439

Take the square root of each side:
x = {-3.096566395, 3.096566395}


Subproblem 2
x2 + -2.5 = -7.088723439

Simplifying
x2 + -2.5 = -7.088723439

Reorder the terms:
-2.5 + x2 = -7.088723439

Solving
-2.5 + x2 = -7.088723439

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x2 = -7.088723439 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x2 = -7.088723439 + 2.5
x2 = -7.088723439 + 2.5

Combine like terms: -7.088723439 + 2.5 = -4.588723439
x2 = -4.588723439

Simplifying
x2 = -4.588723439

Reorder the terms:
4.588723439 + x2 = -4.588723439 + 4.588723439

Combine like terms: -4.588723439 + 4.588723439 = 0.000000000
4.588723439 + 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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