x^4-36=x^2

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Solution for x^4-36=x^2 equation:


Simplifying
x4 + -36 = x2

Reorder the terms:
-36 + x4 = x2

Solving
-36 + x4 = x2

Solving for variable 'x'.

Reorder the terms:
-36 + -1x2 + x4 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + -1x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -1x2 + 36 + x4 = 0 + 36

Reorder the terms:
-36 + 36 + -1x2 + x4 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -1x2 + x4 = 0 + 36
-1x2 + x4 = 0 + 36

Combine like terms: 0 + 36 = 36
-1x2 + x4 = 36

The x term is -1x2.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x2 + 0.25 + x4 = 36 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = 36 + 0.25

Combine like terms: 36 + 0.25 = 36.25
0.25 + -1x2 + x4 = 36.25

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 6.020797289 and -6.020797289.

Subproblem 1

x2 + -0.5 = 6.020797289 Simplifying x2 + -0.5 = 6.020797289 Reorder the terms: -0.5 + x2 = 6.020797289 Solving -0.5 + x2 = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 6.020797289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 6.020797289 + 0.5 x2 = 6.020797289 + 0.5 Combine like terms: 6.020797289 + 0.5 = 6.520797289 x2 = 6.520797289 Simplifying x2 = 6.520797289 Take the square root of each side: x = {-2.553585183, 2.553585183}

Subproblem 2

x2 + -0.5 = -6.020797289 Simplifying x2 + -0.5 = -6.020797289 Reorder the terms: -0.5 + x2 = -6.020797289 Solving -0.5 + x2 = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -6.020797289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -6.020797289 + 0.5 x2 = -6.020797289 + 0.5 Combine like terms: -6.020797289 + 0.5 = -5.520797289 x2 = -5.520797289 Simplifying x2 = -5.520797289 Reorder the terms: 5.520797289 + x2 = -5.520797289 + 5.520797289 Combine like terms: -5.520797289 + 5.520797289 = 0.000000000 5.520797289 + 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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