10x^4-13x^2-4=0

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Solution for 10x^4-13x^2-4=0 equation: 


Simplifying
10x4 + -13x2 + -4 = 0

Reorder the terms:
-4 + -13x2 + 10x4 = 0

Solving
-4 + -13x2 + 10x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
10 the coefficient of the squared term: 

Divide each side by '10'.
-0.4 + -1.3x2 + x4 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -1.3x2 + 0.4 + x4 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -1.3x2 + x4 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -1.3x2 + x4 = 0 + 0.4
-1.3x2 + x4 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-1.3x2 + x4 = 0.4

The x term is -1.3x2.  Take half its coefficient (-0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
-1.3x2 + 0.4225 + x4 = 0.4 + 0.4225

Reorder the terms:
0.4225 + -1.3x2 + x4 = 0.4 + 0.4225

Combine like terms: 0.4 + 0.4225 = 0.8225
0.4225 + -1.3x2 + x4 = 0.8225

Factor a perfect square on the left side:
(x2 + -0.65)(x2 + -0.65) = 0.8225

Calculate the square root of the right side: 0.906917857

Break this problem into two subproblems by setting 
(x2 + -0.65) equal to 0.906917857 and -0.906917857.


Subproblem 1
x2 + -0.65 = 0.906917857

Simplifying
x2 + -0.65 = 0.906917857

Reorder the terms:
-0.65 + x2 = 0.906917857

Solving
-0.65 + x2 = 0.906917857

Solving for variable 'x'.

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

Add '0.65' to each side of the equation.
-0.65 + 0.65 + x2 = 0.906917857 + 0.65

Combine like terms: -0.65 + 0.65 = 0.00
0.00 + x2 = 0.906917857 + 0.65
x2 = 0.906917857 + 0.65

Combine like terms: 0.906917857 + 0.65 = 1.556917857
x2 = 1.556917857

Simplifying
x2 = 1.556917857

Take the square root of each side:
x = {-1.247765145, 1.247765145}


Subproblem 2
x2 + -0.65 = -0.906917857

Simplifying
x2 + -0.65 = -0.906917857

Reorder the terms:
-0.65 + x2 = -0.906917857

Solving
-0.65 + x2 = -0.906917857

Solving for variable 'x'.

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

Add '0.65' to each side of the equation.
-0.65 + 0.65 + x2 = -0.906917857 + 0.65

Combine like terms: -0.65 + 0.65 = 0.00
0.00 + x2 = -0.906917857 + 0.65
x2 = -0.906917857 + 0.65

Combine like terms: -0.906917857 + 0.65 = -0.256917857
x2 = -0.256917857

Simplifying
x2 = -0.256917857

Reorder the terms:
0.256917857 + x2 = -0.256917857 + 0.256917857

Combine like terms: -0.256917857 + 0.256917857 = 0.000000000
0.256917857 + 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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