1000+y^4-110y^2=0

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Solution for 1000+y^4-110y^2=0 equation: 


Simplifying
1000 + y4 + -110y2 = 0

Reorder the terms:
1000 + -110y2 + y4 = 0

Solving
1000 + -110y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(10 + -1y2)(100 + -1y2) = 0

Factor a difference between two squares.
(10 + -1y2)((10 + y)(10 + -1y)) = 0


Subproblem 1
Set the factor '(10 + -1y2)' equal to zero and attempt to solve:

Simplifying
10 + -1y2 = 0

Solving
10 + -1y2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y2 = 0 + -10
-1y2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1y2 = -10

Divide each side by '-1'.
y2 = 10

Simplifying
y2 = 10

Take the square root of each side:
y = {-3.16227766, 3.16227766}

Subproblem 2
Set the factor '(10 + y)' equal to zero and attempt to solve:

Simplifying
10 + y = 0

Solving
10 + y = 0

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

Add '-10' to each side of the equation.
10 + -10 + y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + y = 0 + -10
y = 0 + -10

Combine like terms: 0 + -10 = -10
y = -10

Simplifying
y = -10

Subproblem 3
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10
Solution
y = {-3.16227766, 3.16227766, -10, 10}

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