x^4=169x^2

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Solution for x^4=169x^2 equation:


Simplifying
x4 = 169x2

Solving
x4 = 169x2

Solving for variable 'x'.

Reorder the terms:
-169x2 + x4 = 169x2 + -169x2

Combine like terms: 169x2 + -169x2 = 0
-169x2 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-169 + x2) = 0

Factor a difference between two squares.
x2((13 + x)(-13 + x)) = 0

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}

Subproblem 2

Set the factor '(13 + x)' equal to zero and attempt to solve: Simplifying 13 + x = 0 Solving 13 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + x = 0 + -13 x = 0 + -13 Combine like terms: 0 + -13 = -13 x = -13 Simplifying x = -13

Subproblem 3

Set the factor '(-13 + x)' equal to zero and attempt to solve: Simplifying -13 + x = 0 Solving -13 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + x = 0 + 13 x = 0 + 13 Combine like terms: 0 + 13 = 13 x = 13 Simplifying x = 13

Solution

x = {0, -13, 13}

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