4x^4-17x^2-13=0

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Solution for 4x^4-17x^2-13=0 equation: 


Simplifying
4x4 + -17x2 + -13 = 0

Reorder the terms:
-13 + -17x2 + 4x4 = 0

Solving
-13 + -17x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-3.25 + -4.25x2 + x4 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + -4.25x2 + 3.25 + x4 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + -4.25x2 + x4 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + -4.25x2 + x4 = 0 + 3.25
-4.25x2 + x4 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
-4.25x2 + x4 = 3.25

The x term is -4.25x2.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25x2 + 4.515625 + x4 = 3.25 + 4.515625

Reorder the terms:
4.515625 + -4.25x2 + x4 = 3.25 + 4.515625

Combine like terms: 3.25 + 4.515625 = 7.765625
4.515625 + -4.25x2 + x4 = 7.765625

Factor a perfect square on the left side:
(x2 + -2.125)(x2 + -2.125) = 7.765625

Calculate the square root of the right side: 2.786687101

Break this problem into two subproblems by setting 
(x2 + -2.125) equal to 2.786687101 and -2.786687101.


Subproblem 1
x2 + -2.125 = 2.786687101

Simplifying
x2 + -2.125 = 2.786687101

Reorder the terms:
-2.125 + x2 = 2.786687101

Solving
-2.125 + x2 = 2.786687101

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x2 = 2.786687101 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x2 = 2.786687101 + 2.125
x2 = 2.786687101 + 2.125

Combine like terms: 2.786687101 + 2.125 = 4.911687101
x2 = 4.911687101

Simplifying
x2 = 4.911687101

Take the square root of each side:
x = {-2.216232637, 2.216232637}


Subproblem 2
x2 + -2.125 = -2.786687101

Simplifying
x2 + -2.125 = -2.786687101

Reorder the terms:
-2.125 + x2 = -2.786687101

Solving
-2.125 + x2 = -2.786687101

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x2 = -2.786687101 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x2 = -2.786687101 + 2.125
x2 = -2.786687101 + 2.125

Combine like terms: -2.786687101 + 2.125 = -0.661687101
x2 = -0.661687101

Simplifying
x2 = -0.661687101

Reorder the terms:
0.661687101 + x2 = -0.661687101 + 0.661687101

Combine like terms: -0.661687101 + 0.661687101 = 0.000000000
0.661687101 + 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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