# Solve Using the Square Root Property 3x^2-11x-34=0 3×2-11x-34=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=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 and solve.
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 and solve.
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
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