2y2+30=y2+11

Subtract y2 from both sides of the equation.

2y2+30-y2=11

Subtract y2 from 2y2.

y2+30=11

y2+30=11

Subtract 30 from both sides of the equation.

y2=11-30

Subtract 30 from 11.

y2=-19

y2=-19

Take the square root of both sides of the equation to eliminate the exponent on the left side.

y=±-19

Simplify the right side of the equation.

Rewrite -19 as -1(19).

y=±-1⋅19

Rewrite -1(19) as -1⋅19.

y=±-1⋅19

Rewrite -1 as i.

y=±i19

y=±i19

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

y=i19

Next, use the negative value of the ± to find the second solution.

y=-i19

The complete solution is the result of both the positive and negative portions of the solution.

y=i19,-i19

y=i19,-i19

y=i19,-i19

Solve for y 2y^2+30=y^2+11