Question

Brian is solving the equation x2-3/4x=5. What value must be added to both sides of the equation to make the left side a perfect-square trinomial?

Answer 1

we have

$x^{2} -\frac{3}{4}x=5$

Divide the term  $\frac{3}{4}$ by $2$ and then square it

$(\frac{(3/4)}{2})^{2}= \frac{9}{64}$

Add to both sides

$x^{2} -\frac{3}{4}x+\frac{9}{64}=5+\frac{9}{64}$

Rewrite as perfect square

$(x-\frac{3}{8})^{2}=\frac{329}{64}$

therefore

the answer is

$\frac{9}{64}$

Answer 2

Divide 3/4 by 2 and then square it. 3/4/2=3/8 squared which is 9/64.