Question

What number must be added to the expression below to complete the square x^+5x

Answer 1

Answer:

$\frac{25}{4}$

Step-by-step explanation:

We are given the following expression and we are to complete its square:

$x^2+5x$

To complete the square of the above expression, we will divide the coefficient of x by 2 and add its square to the expression.

Since the coefficient of x here is 5, so we will divide it by 2 and add its square to get:

$x^2+5x+(\frac{5}{2} )^2$

$x^2+5x+\frac{25}{4}$

Therefore, the missing term to complete the square of the given expression is $\frac{25}{4}$.

Answer 2

Answer:

$\frac{25}{4}$

Step-by-step explanation:

The given expression is

$x^2+5x$

Since the coefficient of the quadratic term is 1, you must add the square of $\frac{5}{2}$

which is

$=(\frac{5}{2})^2$

We square both the numerator and the denominator to obtain,

$=\frac{5^2}{2^2}$

This will give us

$=\frac{25}{4}$