Answer
$w=\frac{7}{6}$.
Work Step by Step
The given polynomial is
$\Rightarrow w^2-\frac{7}{3}w+\frac{49}{36}=0$
Multiply each side by $36$.
$\Rightarrow 36(w^2-\frac{7}{3}w+\frac{49}{36})=36(0)$
Use distributive property.
$\Rightarrow 36w^2-84w+49=0$
Write the the polynomial as $a^2-2ab+b^2$.
$\Rightarrow (6w)^2+2(6w)(7)+7^2=0$.
Use perfect square trinomial pattern
$a^2-2ab+b^2=(a-b)^2$.
We have $a=6w$ and $b=7$.
$\Rightarrow (6w-7)^2=0$.
Use zero product property.
$\Rightarrow 6w-7=0$.
Solve for $w$.
$\Rightarrow w=\frac{7}{6}$.
Hence, the solution is $w=\frac{7}{6}$.
