0=4x^4-37x^2+9

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Solution for 0=4x^4-37x^2+9 equation: 


Simplifying
0 = 4x4 + -37x2 + 9

Reorder the terms:
0 = 9 + -37x2 + 4x4

Solving
0 = 9 + -37x2 + 4x4

Solving for variable 'x'.

Combine like terms: 0 + -9 = -9
-9 + 37x2 + -4x4 = 9 + -37x2 + 4x4 + -9 + 37x2 + -4x4

Reorder the terms:
-9 + 37x2 + -4x4 = 9 + -9 + -37x2 + 37x2 + 4x4 + -4x4

Combine like terms: 9 + -9 = 0
-9 + 37x2 + -4x4 = 0 + -37x2 + 37x2 + 4x4 + -4x4
-9 + 37x2 + -4x4 = -37x2 + 37x2 + 4x4 + -4x4

Combine like terms: -37x2 + 37x2 = 0
-9 + 37x2 + -4x4 = 0 + 4x4 + -4x4
-9 + 37x2 + -4x4 = 4x4 + -4x4

Combine like terms: 4x4 + -4x4 = 0
-9 + 37x2 + -4x4 = 0

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

Factor a difference between two squares.
((3 + x)(-3 + x))(1 + -4x2) = 0

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


Subproblem 1
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 2
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 3
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 4
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-3, 3, -0.5, 0.5}

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