x^4-19x^2=48

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Solution for x^4-19x^2=48 equation: 


Simplifying
x4 + -19x2 = 48

Reorder the terms:
-19x2 + x4 = 48

Solving
-19x2 + x4 = 48

Solving for variable 'x'.

Reorder the terms:
-48 + -19x2 + x4 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + -19x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -19x2 + 48 + x4 = 0 + 48

Reorder the terms:
-48 + 48 + -19x2 + x4 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -19x2 + x4 = 0 + 48
-19x2 + x4 = 0 + 48

Combine like terms: 0 + 48 = 48
-19x2 + x4 = 48

The x term is -19x2.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x2 + 90.25 + x4 = 48 + 90.25

Reorder the terms:
90.25 + -19x2 + x4 = 48 + 90.25

Combine like terms: 48 + 90.25 = 138.25
90.25 + -19x2 + x4 = 138.25

Factor a perfect square on the left side:
(x2 + -9.5)(x2 + -9.5) = 138.25

Calculate the square root of the right side: 11.757976016

Break this problem into two subproblems by setting 
(x2 + -9.5) equal to 11.757976016 and -11.757976016.


Subproblem 1
x2 + -9.5 = 11.757976016

Simplifying
x2 + -9.5 = 11.757976016

Reorder the terms:
-9.5 + x2 = 11.757976016

Solving
-9.5 + x2 = 11.757976016

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x2 = 11.757976016 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x2 = 11.757976016 + 9.5
x2 = 11.757976016 + 9.5

Combine like terms: 11.757976016 + 9.5 = 21.257976016
x2 = 21.257976016

Simplifying
x2 = 21.257976016

Take the square root of each side:
x = {-4.610637268, 4.610637268}


Subproblem 2
x2 + -9.5 = -11.757976016

Simplifying
x2 + -9.5 = -11.757976016

Reorder the terms:
-9.5 + x2 = -11.757976016

Solving
-9.5 + x2 = -11.757976016

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x2 = -11.757976016 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x2 = -11.757976016 + 9.5
x2 = -11.757976016 + 9.5

Combine like terms: -11.757976016 + 9.5 = -2.257976016
x2 = -2.257976016

Simplifying
x2 = -2.257976016

Reorder the terms:
2.257976016 + x2 = -2.257976016 + 2.257976016

Combine like terms: -2.257976016 + 2.257976016 = 0.000000000
2.257976016 + 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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