16x^4=89x^2-100

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Solution for 16x^4=89x^2-100 equation: 


Simplifying
16x4 = 89x2 + -100

Reorder the terms:
16x4 = -100 + 89x2

Solving
16x4 = -100 + 89x2

Solving for variable 'x'.

Reorder the terms:
100 + -89x2 + 16x4 = -100 + 89x2 + 100 + -89x2

Reorder the terms:
100 + -89x2 + 16x4 = -100 + 100 + 89x2 + -89x2

Combine like terms: -100 + 100 = 0
100 + -89x2 + 16x4 = 0 + 89x2 + -89x2
100 + -89x2 + 16x4 = 89x2 + -89x2

Combine like terms: 89x2 + -89x2 = 0
100 + -89x2 + 16x4 = 0

Factor a trinomial.
(25 + -16x2)(4 + -1x2) = 0

Factor a difference between two squares.
((5 + 4x)(5 + -4x))(4 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(5 + 4x)(5 + -4x) = 0


Subproblem 1
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 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 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

Subproblem 3
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 4
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
Solution
x = {-1.25, 1.25, -2, 2}

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