9k2+10=-108

Subtract 10 from both sides of the equation.

9k2=-108-10

Subtract 10 from -108.

9k2=-118

9k2=-118

Divide each term in 9k2=-118 by 9.

9k29=-1189

Cancel the common factor of 9.

Cancel the common factor.

9k29=-1189

Divide k2 by 1.

k2=-1189

k2=-1189

Move the negative in front of the fraction.

k2=-1189

k2=-1189

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

k=±-1189

Simplify the right side of the equation.

Rewrite -1189 as (i3)2⋅118.

Rewrite -1 as i2.

k=±i2(1189)

Factor the perfect power 12 out of 118.

k=±i2(12⋅1189)

Factor the perfect power 32 out of 9.

k=±i2(12⋅11832⋅1)

Rearrange the fraction 12⋅11832⋅1.

k=±i2((13)2⋅118)

Rewrite i2(13)2 as (i3)2.

k=±(i3)2⋅118

k=±(i3)2⋅118

Pull terms out from under the radical.

k=±i3⋅118

Combine i3 and 118.

k=±i1183

k=±i1183

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.

k=i1183

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

k=-i1183

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

k=i1183,-i1183

k=i1183,-i1183

k=i1183,-i1183

Solve using the Square Root Property 9k^2+10=-108