(x^4)-(4x^2)+(4)=x^2

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Solution for (x^4)-(4x^2)+(4)=x^2 equation: 


Simplifying
(x4) + -1(4x2) + (4) = x2
x4 + -1(4x2) + (4) = x2

Remove parenthesis around (4x2)
x4 + -1 * 4x2 + (4) = x2

Multiply -1 * 4
x4 + -4x2 + (4) = x2
x4 + -4x2 + 4 = x2

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

Solving
4 + -4x2 + x4 = x2

Solving for variable 'x'.

Reorder the terms:
4 + -4x2 + -1x2 + x4 = x2 + -1x2

Combine like terms: -4x2 + -1x2 = -5x2
4 + -5x2 + x4 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -5x2 + x4 = 0

Factor a trinomial.
(1 + -1x2)(4 + -1x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(4 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(1 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 4
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 1, -2, 2}

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