How do you solve $6x^2 - 27x +27= 0$ by factoring?

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Answer 1 · 2015-08-20T13:13:44

The solutions are
$color(blue)(x=3/2$

$color(blue)(x=3$

$6x^2−27x+27=0$

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 $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 6*27 = 162$
and
$N_1 +N_2 = b = -27$

After trying out a few numbers we get $N_1 = -18$ and $N_2 =-9$
$-18*-9 = 162$ , and $(-18)+(-9)=-27$

$6x^2−27x+27=6x^2−18x-9x+27$
$6x(x-3) -9(x-3) =0$

$(6x-9)(x-3) =0$ is the factorised form of the expression.

We now equate each of these factors to the R.H.S ( $0$ )
$6x-9=0, x=9/6,color(blue)(x=3/2$
$x-3=0, color(blue)(x=3$

How do you solve 6x^2 - 27x +27= 06x^2 - 27x +27= 0 by factoring?