Answer
$c=25$
Work Step by Step
RECALL:
There are two forms of perfect square trinomials:
(1) $m^2+2mn+n^2$, which is the square of $(m+n)^2$; and
(2) $m^2-2mn+n^2$, which is the square of $(m-n)^2$
The given trinomial has:
$m^2 = 49x^2=(7x)^2$, which means that $m=7x$
The middle term of the trinomial is positive therefore the perfect square trinomial will be in the same form as in (1) above.
Thus,
$2mn=70x$
Since $m=7x$, substitute $m$ with $7x$ to obtain:
$2mn=70x
\\-2(7x)(n) = 70x
\\-14x(n) = 70x$
Divide both sides by $-14x$ to obtain:
$\dfrac{-14x(n)}{-14x} = \dfrac{70x}{-14x}
\\n=-5$
The given trinomial is in the form $m^2+2mn+n^2$.
Square $n$ to obtain:
$n^2 = (-5)^2 = 25$
Therefore, the perfect square trinomial is $49x^2+70x+25$.
Hence, $c=25$
