36×2-13x+1=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=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.

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.

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