25x^4=61x^2-36

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Solution for 25x^4=61x^2-36 equation: 


Simplifying
25x4 = 61x2 + -36

Reorder the terms:
25x4 = -36 + 61x2

Solving
25x4 = -36 + 61x2

Solving for variable 'x'.

Reorder the terms:
36 + -61x2 + 25x4 = -36 + 61x2 + 36 + -61x2

Reorder the terms:
36 + -61x2 + 25x4 = -36 + 36 + 61x2 + -61x2

Combine like terms: -36 + 36 = 0
36 + -61x2 + 25x4 = 0 + 61x2 + -61x2
36 + -61x2 + 25x4 = 61x2 + -61x2

Combine like terms: 61x2 + -61x2 = 0
36 + -61x2 + 25x4 = 0

Factor a trinomial.
(1 + -1x2)(36 + -25x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(36 + -25x2) = 0

Factor a difference between two squares.
((6 + 5x)(6 + -5x))(1 + x)(1 + -1x) = 0


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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 3
Set the factor '(6 + 5x)' equal to zero and attempt to solve:

Simplifying
6 + 5x = 0

Solving
6 + 5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = 0 + -6
5x = 0 + -6

Combine like terms: 0 + -6 = -6
5x = -6

Divide each side by '5'.
x = -1.2

Simplifying
x = -1.2

Subproblem 4
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-1, 1, -1.2, 1.2}

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