9x^4=85x^2-196

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Solution for 9x^4=85x^2-196 equation: 


Simplifying
9x4 = 85x2 + -196

Reorder the terms:
9x4 = -196 + 85x2

Solving
9x4 = -196 + 85x2

Solving for variable 'x'.

Reorder the terms:
196 + -85x2 + 9x4 = -196 + 85x2 + 196 + -85x2

Reorder the terms:
196 + -85x2 + 9x4 = -196 + 196 + 85x2 + -85x2

Combine like terms: -196 + 196 = 0
196 + -85x2 + 9x4 = 0 + 85x2 + -85x2
196 + -85x2 + 9x4 = 85x2 + -85x2

Combine like terms: 85x2 + -85x2 = 0
196 + -85x2 + 9x4 = 0

Factor a trinomial.
(4 + -1x2)(49 + -9x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(49 + -9x2) = 0

Factor a difference between two squares.
((7 + 3x)(7 + -3x))(2 + x)(2 + -1x) = 0


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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 4
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-2, 2, -2.333333333, 2.333333333}

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