10X2-11X-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=10⋅-8=-80 and whose sum is b=-11.

Factor -11 out of -11X.

10X2-11X-8=0

Rewrite -11 as 5 plus -16

10X2+(5-16)X-8=0

Apply the distributive property.

10X2+5X-16X-8=0

10X2+5X-16X-8=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(10X2+5X)-16X-8=0

Factor out the greatest common factor (GCF) from each group.

5X(2X+1)-8(2X+1)=0

5X(2X+1)-8(2X+1)=0

Factor the polynomial by factoring out the greatest common factor, 2X+1.

(2X+1)(5X-8)=0

(2X+1)(5X-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.

2X+1=0

5X-8=0

Set the first factor equal to 0.

2X+1=0

Subtract 1 from both sides of the equation.

2X=-1

Divide each term by 2 and simplify.

Divide each term in 2X=-1 by 2.

2X2=-12

Cancel the common factor of 2.

Cancel the common factor.

2X2=-12

Divide X by 1.

X=-12

X=-12

Move the negative in front of the fraction.

X=-12

X=-12

X=-12

Set the next factor equal to 0.

5X-8=0

Add 8 to both sides of the equation.

5X=8

Divide each term by 5 and simplify.

Divide each term in 5X=8 by 5.

5X5=85

Cancel the common factor of 5.

Cancel the common factor.

5X5=85

Divide X by 1.

X=85

X=85

X=85

X=85

The final solution is all the values that make (2X+1)(5X-8)=0 true.

X=-12,85

Solve using the Square Root Property 10X^2-11X-8=0