4x^4=53x^2-49

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Solution for 4x^4=53x^2-49 equation: 


Simplifying
4x4 = 53x2 + -49

Reorder the terms:
4x4 = -49 + 53x2

Solving
4x4 = -49 + 53x2

Solving for variable 'x'.

Reorder the terms:
49 + -53x2 + 4x4 = -49 + 53x2 + 49 + -53x2

Reorder the terms:
49 + -53x2 + 4x4 = -49 + 49 + 53x2 + -53x2

Combine like terms: -49 + 49 = 0
49 + -53x2 + 4x4 = 0 + 53x2 + -53x2
49 + -53x2 + 4x4 = 53x2 + -53x2

Combine like terms: 53x2 + -53x2 = 0
49 + -53x2 + 4x4 = 0

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

Factor a difference between two squares.
((1 + x)(1 + -1x))(49 + -4x2) = 0

Factor a difference between two squares.
((7 + 2x)(7 + -2x))(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 '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 4
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-1, 1, -3.5, 3.5}

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