# How do you solve x^2=12x-27?

May 23, 2015

${x}^{2} = 12 x - 27$
${x}^{2} - 12 x + 27 = 0$

We can Split the Middle Term of this expression to factorise it and thereby find the solution.
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 = -12

After trying out a few numbers we get ${N}_{1} = - 9$ and ${N}_{2} = - 3$
$9 \cdot 3 = 27$, and $- 9 + \left(- 3\right) = - 12$

${x}^{2} - 12 x + 27 = {x}^{2} - 9 x - 3 x + 27$
$x \left(x - 9\right) - 3 \left(x - 9\right) = 0$

color(green)((x-9)(x - 3) is the factorised form.
and color(green)(x=9 and x=3# are the solutions.