x^4-5x^2=4

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Solution for x^4-5x^2=4 equation:


Simplifying
x4 + -5x2 = 4

Reorder the terms:
-5x2 + x4 = 4

Solving
-5x2 + x4 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + -5x2 + x4 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -5x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -5x2 + 4 + x4 = 0 + 4

Reorder the terms:
-4 + 4 + -5x2 + x4 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x2 + x4 = 0 + 4
-5x2 + x4 = 0 + 4

Combine like terms: 0 + 4 = 4
-5x2 + x4 = 4

The x term is -5x2.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x2 + 6.25 + x4 = 4 + 6.25

Reorder the terms:
6.25 + -5x2 + x4 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + -5x2 + x4 = 10.25

Factor a perfect square on the left side:
(x2 + -2.5)(x2 + -2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x2 + -2.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x2 + -2.5 = 3.201562119 Simplifying x2 + -2.5 = 3.201562119 Reorder the terms: -2.5 + x2 = 3.201562119 Solving -2.5 + x2 = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 3.201562119 + 2.5 x2 = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 x2 = 5.701562119 Simplifying x2 = 5.701562119 Take the square root of each side: x = {-2.387794405, 2.387794405}

Subproblem 2

x2 + -2.5 = -3.201562119 Simplifying x2 + -2.5 = -3.201562119 Reorder the terms: -2.5 + x2 = -3.201562119 Solving -2.5 + x2 = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -3.201562119 + 2.5 x2 = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 x2 = -0.701562119 Simplifying x2 = -0.701562119 Reorder the terms: 0.701562119 + x2 = -0.701562119 + 0.701562119 Combine like terms: -0.701562119 + 0.701562119 = 0.000000000 0.701562119 + 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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