# Solve Using the Square Root Property 18x^2+11x-10=0 18×2+11x-10=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=18⋅-10=-180 and whose sum is b=11.
Factor 11 out of 11x.
18×2+11(x)-10=0
Rewrite 11 as -9 plus 20
18×2+(-9+20)x-10=0
Apply the distributive property.
18×2-9x+20x-10=0
18×2-9x+20x-10=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(18×2-9x)+20x-10=0
Factor out the greatest common factor (GCF) from each group.
9x(2x-1)+10(2x-1)=0
9x(2x-1)+10(2x-1)=0
Factor the polynomial by factoring out the greatest common factor, 2x-1.
(2x-1)(9x+10)=0
(2x-1)(9x+10)=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
9x+10=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
2x-1=0
Add 1 to both sides of the equation.
2x=1
Divide each term by 2 and simplify.
Divide each term in 2x=1 by 2.
2×2=12
Cancel the common factor of 2.
Cancel the common factor.
2×2=12
Divide x by 1.
x=12
x=12
x=12
x=12
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
9x+10=0
Subtract 10 from both sides of the equation.
9x=-10
Divide each term by 9 and simplify.
Divide each term in 9x=-10 by 9.
9×9=-109
Cancel the common factor of 9.
Cancel the common factor.
9×9=-109
Divide x by 1.
x=-109
x=-109
Move the negative in front of the fraction.
x=-109
x=-109
x=-109
The final solution is all the values that make (2x-1)(9x+10)=0 true.
x=12,-109
Solve Using the Square Root Property 18x^2+11x-10=0     