2-20y2=17

Subtract 2 from both sides of the equation.

-20y2=17-2

Subtract 2 from 17.

-20y2=15

-20y2=15

Divide each term in -20y2=15 by -20.

-20y2-20=15-20

Cancel the common factor of -20.

Cancel the common factor.

-20y2-20=15-20

Divide y2 by 1.

y2=15-20

y2=15-20

Simplify 15-20.

Cancel the common factor of 15 and -20.

Factor 5 out of 15.

y2=5(3)-20

Cancel the common factors.

Factor 5 out of -20.

y2=5⋅35⋅-4

Cancel the common factor.

y2=5⋅35⋅-4

Rewrite the expression.

y2=3-4

y2=3-4

y2=3-4

Move the negative in front of the fraction.

y2=-34

y2=-34

y2=-34

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

y=±-34

Simplify the right side of the equation.

Rewrite -34 as (i2)2⋅3.

Rewrite -1 as i2.

y=±i2(34)

Factor the perfect power 12 out of 3.

y=±i2(12⋅34)

Factor the perfect power 22 out of 4.

y=±i2(12⋅322⋅1)

Rearrange the fraction 12⋅322⋅1.

y=±i2((12)2⋅3)

Rewrite i2(12)2 as (i2)2.

y=±(i2)2⋅3

y=±(i2)2⋅3

Pull terms out from under the radical.

y=±i2⋅3

Combine i2 and 3.

y=±i32

y=±i32

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=i32

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

y=-i32

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

y=i32,-i32

y=i32,-i32

y=i32,-i32

Solve Using the Square Root Property 2-20y^2=17