# Solve using the Square Root Property 9k^2+10=-108 9k2+10=-108
Move all terms not containing k to the right side of the equation.
Subtract 10 from both sides of the equation.
9k2=-108-10
Subtract 10 from -108.
9k2=-118
9k2=-118
Divide each term by 9 and simplify.
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
The complete solution is the result of both the positive and negative portions of the solution.
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     