The square of half the x-coefficient must be added. That value is
... ((1/2)·(-3/4))² = (-3/8)² =
... A) 9/64
Answer:
[tex]\frac{9}{64}\text{ is added to both sides of the equation to make the left side a perfect-square trinomial.}[/tex]
Step-by-step explanation:
Given the equation
[tex]x^2-\frac{3}{4}x=5[/tex]
we have to find the value which must be added to both sides of the equation to make the left side a perfect-square trinomial.
[tex]x^2-\frac{3}{4}x=5[/tex]
To form the perfect square we have to add the square of half the coefficient of x,
[tex]\text{Here the coefficient of x is }(-\frac{3}{4})[/tex]
[tex]\text{Now, the square of half of above is }(-\frac{3}{8})^2=\frac{9}{64}[/tex]
[tex]x^2-2(x)(\frac{3}{8})+\frac{9}{64}=5+\frac{9}{64}[/tex]
[tex]x^2-2(x)(\frac{3}{8})+(-\frac{3}{8})^2=5+\frac{9}{64}[/tex]
[tex](x-\frac{3}{8})^2=5+\frac{9}{64}[/tex]
which makes LHS a perfect square trinomial.
[tex]\frac{9}{64}\text{ is added to both sides of the equation to make the left side a perfect-square trinomial.}[/tex]
