# How do you solve x^2-6x-27 = 0?

Aug 20, 2015

The solutions are
 color(blue)(x=-3

 color(blue)(x=9

#### Explanation:

x^2−6x−27=0

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 27 = - 27$
and
${N}_{1} + {N}_{2} = b = - 6$

After trying out a few numbers we get ${N}_{1} = - 9$ and ${N}_{2} = 3$
$- 9 \cdot 3 = - 27$, and $3 + \left(- 9\right) = - 6$

x^2−6x−27=x^2−9x+3x−27

x^2−9x+3x−27=0

x(x−9)+3(x−9)=0
(x+3) (x−9)=0 is the factorised form of the expression.

Now we equate these factors to the R.H.S ($0$)
x+3=0, color(blue)(x=-3

x-9=0, color(blue)(x=9

Aug 20, 2015

Solve y = x^2 - 6x - 27 = 0

Ans: -3 and 9

#### Explanation:

x^2 - 6x - 27 = 0
Find 2 numbers knowing sum (6) and product (-27). Roots have opposite signs.
Factor pairs of -27 --> (-1, 27)(-3, 9). This last sum is 6 = -b. Therefor, the 2 real roots are: -3 and 9.