49x^5-25x^3+x^2=x^2

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Solution for 49x^5-25x^3+x^2=x^2 equation: 


Simplifying
49x5 + -25x3 + x2 = x2

Reorder the terms:
x2 + -25x3 + 49x5 = x2

Add '-1x2' to each side of the equation.
x2 + -25x3 + -1x2 + 49x5 = x2 + -1x2

Reorder the terms:
x2 + -1x2 + -25x3 + 49x5 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -25x3 + 49x5 = x2 + -1x2
-25x3 + 49x5 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-25x3 + 49x5 = 0

Solving
-25x3 + 49x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-25 + 49x2) = 0

Factor a difference between two squares.
x3((5 + 7x)(-5 + 7x)) = 0


Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

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 + 7x)' equal to zero and attempt to solve:

Simplifying
5 + 7x = 0

Solving
5 + 7x = 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 + 7x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7x = 0 + -5
7x = 0 + -5

Combine like terms: 0 + -5 = -5
7x = -5

Divide each side by '7'.
x = -0.7142857143

Simplifying
x = -0.7142857143

Subproblem 3
Set the factor '(-5 + 7x)' equal to zero and attempt to solve:

Simplifying
-5 + 7x = 0

Solving
-5 + 7x = 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 + 7x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 7x = 0 + 5
7x = 0 + 5

Combine like terms: 0 + 5 = 5
7x = 5

Divide each side by '7'.
x = 0.7142857143

Simplifying
x = 0.7142857143
Solution
x = {-0.7142857143, 0.7142857143}

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