9k2-71k-8=0

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.

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.

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