18×2+11x-10=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=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.

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.

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