0=x^4+10x^2+25

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Solution for 0=x^4+10x^2+25 equation:


Simplifying
0 = x4 + 10x2 + 25

Reorder the terms:
0 = 25 + 10x2 + x4

Solving
0 = 25 + 10x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -25 = -25
-25 + -10x2 + -1x4 = 25 + 10x2 + x4 + -25 + -10x2 + -1x4

Reorder the terms:
-25 + -10x2 + -1x4 = 25 + -25 + 10x2 + -10x2 + x4 + -1x4

Combine like terms: 25 + -25 = 0
-25 + -10x2 + -1x4 = 0 + 10x2 + -10x2 + x4 + -1x4
-25 + -10x2 + -1x4 = 10x2 + -10x2 + x4 + -1x4

Combine like terms: 10x2 + -10x2 = 0
-25 + -10x2 + -1x4 = 0 + x4 + -1x4
-25 + -10x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-25 + -10x2 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(25 + 10x2 + x4) = 0

Factor a trinomial.
-1((5 + x2)(5 + x2)) = 0

Ignore the factor -1.

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 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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