0=x^4-34x^2+225

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Solution for 0=x^4-34x^2+225 equation: 


Simplifying
0 = x4 + -34x2 + 225

Reorder the terms:
0 = 225 + -34x2 + x4

Solving
0 = 225 + -34x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -225 = -225
-225 + 34x2 + -1x4 = 225 + -34x2 + x4 + -225 + 34x2 + -1x4

Reorder the terms:
-225 + 34x2 + -1x4 = 225 + -225 + -34x2 + 34x2 + x4 + -1x4

Combine like terms: 225 + -225 = 0
-225 + 34x2 + -1x4 = 0 + -34x2 + 34x2 + x4 + -1x4
-225 + 34x2 + -1x4 = -34x2 + 34x2 + x4 + -1x4

Combine like terms: -34x2 + 34x2 = 0
-225 + 34x2 + -1x4 = 0 + x4 + -1x4
-225 + 34x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-225 + 34x2 + -1x4 = 0

Factor a trinomial.
(-25 + x2)(9 + -1x2) = 0

Factor a difference between two squares.
((5 + x)(-5 + x))(9 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(5 + x)(-5 + x) = 0


Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

Subproblem 4
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-5, 5, -3, 3}

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