# Solve Using the Square Root Property 36x^2-13x+1=0 36×2-13x+1=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=36⋅1=36 and whose sum is b=-13.
Factor -13 out of -13x.
36×2-13x+1=0
Rewrite -13 as -4 plus -9
36×2+(-4-9)x+1=0
Apply the distributive property.
36×2-4x-9x+1=0
36×2-4x-9x+1=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(36×2-4x)-9x+1=0
Factor out the greatest common factor (GCF) from each group.
4x(9x-1)-(9x-1)=0
4x(9x-1)-(9x-1)=0
Factor the polynomial by factoring out the greatest common factor, 9x-1.
(9x-1)(4x-1)=0
(9x-1)(4x-1)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
9x-1=0
4x-1=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
9x-1=0
Add 1 to both sides of the equation.
9x=1
Divide each term by 9 and simplify.
Divide each term in 9x=1 by 9.
9×9=19
Cancel the common factor of 9.
Cancel the common factor.
9×9=19
Divide x by 1.
x=19
x=19
x=19
x=19
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
4x-1=0
Add 1 to both sides of the equation.
4x=1
Divide each term by 4 and simplify.
Divide each term in 4x=1 by 4.
4×4=14
Cancel the common factor of 4.
Cancel the common factor.
4×4=14
Divide x by 1.
x=14
x=14
x=14
x=14
The final solution is all the values that make (9x-1)(4x-1)=0 true.
x=19,14
Solve Using the Square Root Property 36x^2-13x+1=0     