Answer
$\left\{-\frac{5}{4}\right\}$
Work Step by Step
The equation can be written as:
$(4y)^2+2(4y)(5) + 5^2=0$
The left side of the equation is a perfect square trinomial of the form $a^2+2ab+b^2$ where $a=4y$ and $b=5$.
RECALL:
$a^2+2ab+b^2=(a+b)^2$
Factor the trinomial using the formula above with $a=4y$ and $b=5$ to obtain:
$(4y+5)^2=0$
Equate the factor to 0 to obtain:
$4y+5=0$
Solve the equation to obtain:
$4y=-5
\\y=\frac{-5}{4}$
Therefore the solution set is $\left\{-\frac{5}{4}\right\}$.
