X^4-25=0

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Solution for X^4-25=0 equation:


Simplifying
X4 + -25 = 0

Reorder the terms:
-25 + X4 = 0

Solving
-25 + X4 = 0

Solving for variable 'X'.

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

Add '25' to each side of the equation.
-25 + 25 + X4 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + X4 = 0 + 25
X4 = 0 + 25

Combine like terms: 0 + 25 = 25
X4 = 25

Simplifying
X4 = 25

Reorder the terms:
-25 + X4 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + X4 = 0

Factor a difference between two squares.
(5 + X2)(-5 + X2) = 0

Subproblem 1

Set the factor '(5 + X2)' equal to zero and attempt to solve: Simplifying 5 + X2 = 0 Solving 5 + X2 = 0 Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + X2 = 0 + -5 X2 = 0 + -5 Combine like terms: 0 + -5 = -5 X2 = -5 Simplifying X2 = -5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-5 + X2)' equal to zero and attempt to solve: Simplifying -5 + X2 = 0 Solving -5 + X2 = 0 Move all terms containing X to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + X2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + X2 = 0 + 5 X2 = 0 + 5 Combine like terms: 0 + 5 = 5 X2 = 5 Simplifying X2 = 5 Take the square root of each side: X = {-2.236067978, 2.236067978}

Solution

X = {-2.236067978, 2.236067978}

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