# Solve Using the Square Root Property 3x^2-17x+10=0 3×2-17x+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=3⋅10=30 and whose sum is b=-17.
Factor -17 out of -17x.
3×2-17x+10=0
Rewrite -17 as -2 plus -15
3×2+(-2-15)x+10=0
Apply the distributive property.
3×2-2x-15x+10=0
3×2-2x-15x+10=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(3×2-2x)-15x+10=0
Factor out the greatest common factor (GCF) from each group.
x(3x-2)-5(3x-2)=0
x(3x-2)-5(3x-2)=0
Factor the polynomial by factoring out the greatest common factor, 3x-2.
(3x-2)(x-5)=0
(3x-2)(x-5)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
3x-2=0
x-5=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
3x-2=0
Add 2 to both sides of the equation.
3x=2
Divide each term by 3 and simplify.
Divide each term in 3x=2 by 3.
3×3=23
Cancel the common factor of 3.
Cancel the common factor.
3×3=23
Divide x by 1.
x=23
x=23
x=23
x=23
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
x-5=0
Add 5 to both sides of the equation.
x=5
x=5
The final solution is all the values that make (3x-2)(x-5)=0 true.
x=23,5
Solve Using the Square Root Property 3x^2-17x+10=0     