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

10X2-11X-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=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 and solve.
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 and solve.
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