How do you factor and solve $6b^2 - 13b + 3 = -3$ ?

Question

How do you factor and solve $6b^2 - 13b + 3 = -3$ ?

1 Answer

Impact of this question

3806 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-03-28T14:34:16

Rewrite $6b^2 - 13b + 3 = -3$
as
$6b^2-13b+6=0$

Assuming only integer values appear in the factoring (not necessarily true, but easier if it is)
we are looking for integer values for $p$ , $q$ , $r$ , and $s$ (all $>= 0$ )
such that
$(pb-q)(rb-s) = 6b^2-13b+6$
(the negative sign on the coefficient $-13$ tells us that at least one of the internal signs in the factors is negative, assuming positive values for $p, q, r, s$
and the positive sign on $+6$ tells us that the internal signs are the same i.e. they are both negative).

$(pb-q)(rb-s) = (pbr)b^2 - (ps+qr)b + qs$
$rarr pb = 6$
$rarr ps+qr = 13$
$rarr qs = 6$

Since the only positive integer factors of $6$ are $6xx1$ and $3xx2$

It is a fairly simply matter to discover
$p=3$
$q=2$
$r=3$
$s=2$

That is
$(3b-2)^2 = 6b^2-12b+6 = 0$

Which implies there is only one solution ( $3b-2=0$ )
$b=2/3$

Science

Math

Humanities

... and beyond

How do you factor and solve $6b^2 - 13b + 3 = -3$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you factor and solve 6b^2 - 13b + 3 = -36b^2 - 13b + 3 = -3?

1 Answer

Related questions

Impact of this question

How do you factor and solve $6b^2 - 13b + 3 = -3$ ?