brian is solving the equation $x^{2}-\frac{3}{4}x = 5$. what value must be added to both sides of the…

brian is solving the equation $x^{2}-\frac{3}{4}x = 5$. what value must be added to both sides of the equation to make the left side a perfect - square trinomial?\n$\frac{9}{64}$\n$\frac{9}{16}$\n$\frac{3}{4}$\n$\frac{9}{4}$

brian is solving the equation $x^{2}-\frac{3}{4}x = 5$. what value must be added to both sides of the equation to make the left side a perfect - square trinomial?\n$\frac{9}{64}$\n$\frac{9}{16}$\n$\frac{3}{4}$\n$\frac{9}{4}$

Answer

Explanation:

Step1: Recall the formula for perfect - square trinomial

For a quadratic expression of the form $x^{2}+bx$, to make it a perfect - square trinomial, we add $\left(\frac{b}{2}\right)^{2}$. In the given equation $x^{2}-\frac{3}{4}x = 5$, here $b=-\frac{3}{4}$.

Step2: Calculate $\left(\frac{b}{2}\right)^{2}$

First, find $\frac{b}{2}$, where $b =-\frac{3}{4}$, so $\frac{b}{2}=\frac{-\frac{3}{4}}{2}=-\frac{3}{8}$. Then, square it: $\left(-\frac{3}{8}\right)^{2}=\frac{9}{64}$.

Answer:

A. $\frac{9}{64}$