Answer
$y=(\frac{5+\sqrt 17}{2}, \frac{5-\sqrt 17}{2})$
Work Step by Step
Step-1 : Since there is no constant side on the right side, we subtract 2 from both sides.
Therefore the equation becomes $y^2-5y=-2$
Step -2 : Add the square of half of the co-efficient of x to both sides.
Co-efficient of y = -5
Half of -5 = $\frac{1}{2}\times-5 = \frac{-5}{2}$
Square of $\frac{-5}{2}$ is $\frac{-5}{2} \times\frac{-5}{2} = \frac{25}{4}$
The equation becomes $y^2-5y+\frac{25}{4}=-2 +\frac{25}{4}$
Step-3 Factor the trinomial and simplify the right hand side.
$(y-\frac{5}{2})^2= \frac{-8+25}{4}$
$(y-\frac{5}{2})^2= \frac{-17}{4}$
Step-4 Use the square root property and solve for y
$y-\frac{5}{2}=±\sqrt \frac{17}{4}$
$y-\frac{5}{2}=±\frac{\sqrt 17}{2}$
Step-5 Add $\frac{5}{2}$ on both the sides
$y=\frac{5}{2}±\frac{\sqrt 17}{2}$
$y=\frac{5±\sqrt 17}{2}$
Therefore the solution set is $(\frac{5+\sqrt 17}{2}, \frac{5-\sqrt 17}{2})$
