3×2-11x-34=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=3⋅-34=-102 and whose sum is b=-11.

Factor -11 out of -11x.

3×2-11x-34=0

Rewrite -11 as 6 plus -17

3×2+(6-17)x-34=0

Apply the distributive property.

3×2+6x-17x-34=0

3×2+6x-17x-34=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(3×2+6x)-17x-34=0

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

3x(x+2)-17(x+2)=0

3x(x+2)-17(x+2)=0

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

(x+2)(3x-17)=0

(x+2)(3x-17)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x+2=0

3x-17=0

Set the first factor equal to 0.

x+2=0

Subtract 2 from both sides of the equation.

x=-2

x=-2

Set the next factor equal to 0.

3x-17=0

Add 17 to both sides of the equation.

3x=17

Divide each term by 3 and simplify.

Divide each term in 3x=17 by 3.

3×3=173

Cancel the common factor of 3.

Cancel the common factor.

3×3=173

Divide x by 1.

x=173

x=173

x=173

x=173

The final solution is all the values that make (x+2)(3x-17)=0 true.

x=-2,173

Solve Using the Square Root Property 3x^2-11x-34=0