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

2-20y2=17
Move all terms not containing y to the right side of the equation.
Subtract 2 from both sides of the equation.
-20y2=17-2
Subtract 2 from 17.
-20y2=15
-20y2=15
Divide each term by -20 and simplify.
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
The complete solution is the result of both the positive and negative portions of the solution.
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