Question

Brian is solving the equation x squared minus three-fourths x = 5. What value must be added to both sides of the equation to make the left side a perfect-square trinomial?

Answer 1

Answer:

$\dfrac{9}{64}$

Step-by-step explanation:

Given the equation: $x^2-\frac{3}{4}x=5$

To make the left hand side of the equation a perfect trinomial, we follow these steps.

Step 1: Divide the coefficient of x by 2.

Coefficient of x $=-\frac{3}{4}$

$-\frac{3}{4} \div 2 =-\frac{3}{8}$

Step 2: Square your result from step 1

$\implies (-\frac{3}{8})^2 \\=\dfrac{9}{64}$

Therefore, to make the Left-Hand side a  perfect-square trinomial, we add 9/64.

Answer 2

Answer:

Term to add is (3/8)^2 = 9/64

Step-by-step explanation:

Here, we want to know the value that must be added to make the equation a perfect square.

x^2 - 3/4x = 5

x^2 -3/4x -(3/8)^2+ (3/8)^2 = 5

x^2 -3/4x + (3/8)^2 = 5 + (3/8)^2

= (x-3/8)^2 = 5 + (3/8)^2

So the term to add is (3/8)^2 = 9/64