# Solve using the Square Root Property 7x^2-12x-27=0 7×2-12x-27=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=7⋅-27=-189 and whose sum is b=-12.
Factor -12 out of -12x.
7×2-12x-27=0
Rewrite -12 as 9 plus -21
7×2+(9-21)x-27=0
Apply the distributive property.
7×2+9x-21x-27=0
7×2+9x-21x-27=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(7×2+9x)-21x-27=0
Factor out the greatest common factor (GCF) from each group.
x(7x+9)-3(7x+9)=0
x(7x+9)-3(7x+9)=0
Factor the polynomial by factoring out the greatest common factor, 7x+9.
(7x+9)(x-3)=0
(7x+9)(x-3)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
7x+9=0
x-3=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
7x+9=0
Subtract 9 from both sides of the equation.
7x=-9
Divide each term by 7 and simplify.
Divide each term in 7x=-9 by 7.
7×7=-97
Cancel the common factor of 7.
Cancel the common factor.
7×7=-97
Divide x by 1.
x=-97
x=-97
Move the negative in front of the fraction.
x=-97
x=-97
x=-97
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
x-3=0
Add 3 to both sides of the equation.
x=3
x=3
The final solution is all the values that make (7x+9)(x-3)=0 true.
x=-97,3
Solve using the Square Root Property 7x^2-12x-27=0     