(x^4)-(5x^2)+(4)=0

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Solution for (x^4)-(5x^2)+(4)=0 equation:


Simplifying
(x4) + -1(5x2) + (4) = 0
x4 + -1(5x2) + (4) = 0

Remove parenthesis around (5x2)
x4 + -1 * 5x2 + (4) = 0

Multiply -1 * 5
x4 + -5x2 + (4) = 0
x4 + -5x2 + 4 = 0

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

Solving
4 + -5x2 + x4 = 0

Solving for variable 'x'.

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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