# Solve using the Square Root Property 9k^2-71k-8=0

9k2-71k-8=0
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=9⋅-8=-72 and whose sum is b=-71.
Factor -71 out of -71k.
9k2-71k-8=0
Rewrite -71 as 1 plus -72
9k2+(1-72)k-8=0
Apply the distributive property.
9k2+1k-72k-8=0
Multiply k by 1.
9k2+k-72k-8=0
9k2+k-72k-8=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(9k2+k)-72k-8=0
Factor out the greatest common factor (GCF) from each group.
k(9k+1)-8(9k+1)=0
k(9k+1)-8(9k+1)=0
Factor the polynomial by factoring out the greatest common factor, 9k+1.
(9k+1)(k-8)=0
(9k+1)(k-8)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
9k+1=0
k-8=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
9k+1=0
Subtract 1 from both sides of the equation.
9k=-1
Divide each term by 9 and simplify.
Divide each term in 9k=-1 by 9.
9k9=-19
Cancel the common factor of 9.
Cancel the common factor.
9k9=-19
Divide k by 1.
k=-19
k=-19
Move the negative in front of the fraction.
k=-19
k=-19
k=-19
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
k-8=0
Add 8 to both sides of the equation.
k=8
k=8
The final solution is all the values that make (9k+1)(k-8)=0 true.
k=-19,8
Solve using the Square Root Property 9k^2-71k-8=0