x^4=13x^2+36

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Solution for x^4=13x^2+36 equation: 


Simplifying
x4 = 13x2 + 36

Reorder the terms:
x4 = 36 + 13x2

Solving
x4 = 36 + 13x2

Solving for variable 'x'.

Reorder the terms:
-36 + -13x2 + x4 = 36 + 13x2 + -36 + -13x2

Reorder the terms:
-36 + -13x2 + x4 = 36 + -36 + 13x2 + -13x2

Combine like terms: 36 + -36 = 0
-36 + -13x2 + x4 = 0 + 13x2 + -13x2
-36 + -13x2 + x4 = 13x2 + -13x2

Combine like terms: 13x2 + -13x2 = 0
-36 + -13x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -13x2 + 36 + x4 = 0 + 36

Reorder the terms:
-36 + 36 + -13x2 + x4 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -13x2 + x4 = 0 + 36
-13x2 + x4 = 0 + 36

Combine like terms: 0 + 36 = 36
-13x2 + x4 = 36

The x term is -13x2.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x2 + 42.25 + x4 = 36 + 42.25

Reorder the terms:
42.25 + -13x2 + x4 = 36 + 42.25

Combine like terms: 36 + 42.25 = 78.25
42.25 + -13x2 + x4 = 78.25

Factor a perfect square on the left side:
(x2 + -6.5)(x2 + -6.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(x2 + -6.5) equal to 8.845903006 and -8.845903006.


Subproblem 1
x2 + -6.5 = 8.845903006

Simplifying
x2 + -6.5 = 8.845903006

Reorder the terms:
-6.5 + x2 = 8.845903006

Solving
-6.5 + x2 = 8.845903006

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x2 = 8.845903006 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x2 = 8.845903006 + 6.5
x2 = 8.845903006 + 6.5

Combine like terms: 8.845903006 + 6.5 = 15.345903006
x2 = 15.345903006

Simplifying
x2 = 15.345903006

Take the square root of each side:
x = {-3.917384715, 3.917384715}


Subproblem 2
x2 + -6.5 = -8.845903006

Simplifying
x2 + -6.5 = -8.845903006

Reorder the terms:
-6.5 + x2 = -8.845903006

Solving
-6.5 + x2 = -8.845903006

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x2 = -8.845903006 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x2 = -8.845903006 + 6.5
x2 = -8.845903006 + 6.5

Combine like terms: -8.845903006 + 6.5 = -2.345903006
x2 = -2.345903006

Simplifying
x2 = -2.345903006

Reorder the terms:
2.345903006 + x2 = -2.345903006 + 2.345903006

Combine like terms: -2.345903006 + 2.345903006 = 0.000000000
2.345903006 + 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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