x^4+x^2+4=80

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Solution for x^4+x^2+4=80 equation:


Simplifying
x4 + x2 + 4 = 80

Reorder the terms:
4 + x2 + x4 = 80

Solving
4 + x2 + x4 = 80

Solving for variable 'x'.

Reorder the terms:
4 + -80 + x2 + x4 = 80 + -80

Combine like terms: 4 + -80 = -76
-76 + x2 + x4 = 80 + -80

Combine like terms: 80 + -80 = 0
-76 + x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '76' to each side of the equation.
-76 + x2 + 76 + x4 = 0 + 76

Reorder the terms:
-76 + 76 + x2 + x4 = 0 + 76

Combine like terms: -76 + 76 = 0
0 + x2 + x4 = 0 + 76
x2 + x4 = 0 + 76

Combine like terms: 0 + 76 = 76
x2 + x4 = 76

The x term is x2.  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.
x2 + 0.25 + x4 = 76 + 0.25

Reorder the terms:
0.25 + x2 + x4 = 76 + 0.25

Combine like terms: 76 + 0.25 = 76.25
0.25 + x2 + x4 = 76.25

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 76.25

Calculate the square root of the right side: 8.732124598

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 8.732124598 and -8.732124598.

Subproblem 1

x2 + 0.5 = 8.732124598 Simplifying x2 + 0.5 = 8.732124598 Reorder the terms: 0.5 + x2 = 8.732124598 Solving 0.5 + x2 = 8.732124598 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 = 8.732124598 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 8.732124598 + -0.5 x2 = 8.732124598 + -0.5 Combine like terms: 8.732124598 + -0.5 = 8.232124598 x2 = 8.232124598 Simplifying x2 = 8.232124598 Take the square root of each side: x = {-2.869167928, 2.869167928}

Subproblem 2

x2 + 0.5 = -8.732124598 Simplifying x2 + 0.5 = -8.732124598 Reorder the terms: 0.5 + x2 = -8.732124598 Solving 0.5 + x2 = -8.732124598 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 = -8.732124598 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -8.732124598 + -0.5 x2 = -8.732124598 + -0.5 Combine like terms: -8.732124598 + -0.5 = -9.232124598 x2 = -9.232124598 Simplifying x2 = -9.232124598 Reorder the terms: 9.232124598 + x2 = -9.232124598 + 9.232124598 Combine like terms: -9.232124598 + 9.232124598 = 0.000000000 9.232124598 + 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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