Question

What number must you add to the polynomial below to complete the square? x2 + 15x

Answer 1

Answer:

The number $\frac{225}{4}$ is added to the polynomial below to complete the square.

Step-by-step explanation:

Perfect square binomial:

A perfect square binomial is given by:

$(a + b)^2 = a^2 + 2ab + b^2$

In this question:

We have that:

$a^2 + 2ab + b^2 = x^2 + 15x + ?$

Since $a = x$, we have that:

$2ab = 15x$

$2b = 15$

$b = \frac{15}{2}$

Completing the square:

The term that completes the square is $b^2$. So

$b^2 = (\frac{15}{2})^2 = \frac{225}{4}$

The number $\frac{225}{4}$ is added to the polynomial below to complete the square.