# How do you factor the expression #x^2-x-36#?

##### 1 Answer

#### Answer:

Use the quadratic formula to find:

#x^2-x-36 = (x-(1-sqrt(145))/2)(x-(1+sqrt(145))/2)#

#### Explanation:

You would like to find a pair of factors of

Let's check the discriminant:

#Delta = b^2-4ac = (-1)^2-(4*1*-36) = 1+144 = 145#

Since this is positive but not a perfect square, the quadratic has factors with Real irrational coefficients.

We can find these factors using the quadratic formula. The zeros of the quadratic are given by:

#x = (-b+-sqrt(b^2-4ac))/(2a) = (-b+-sqrt(Delta))/(2a)#

#=(1+-sqrt(145))/2#

That is

So:

#x^2-x-36 = (x-x_1)(x-x_2) = (x-(1-sqrt(145))/2)(x-(1+sqrt(145))/2)#