Question

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n2+5/2n

Answer 1

Answer:

$n^2 + \frac{5}{2}n + \frac{25}{16}$

$(n + \frac{5}{4})^2$

Step-by-step explanation:

Given

$n^2 + \frac{5}{2}n$

Required

(a) Make a perfect square trinomial

(b) Write as binomial square

Solving (a)

Let the missing part of the expression be k;

This gives

$n^2 + \frac{5}{2}n + k$

To solve for k, we need to square half the coefficient of n;

i.e. Since the coefficient of n is $\frac{5}{2}$, then

$k = (\frac{1}{2} * \frac{5}{2})^2$

$k = (\frac{5}{4})^2$

$k = \frac{25}{16}$

Hence;

$n^2 + \frac{5}{2}n + k$ = $n^2 + \frac{5}{2}n + \frac{25}{16}$

Solving (b)

$n^2 + \frac{5}{2}n + \frac{25}{16}$

Expand $\frac{5}{2}n$

$n^2 + \frac{5}{4}n+ \frac{5}{4}n + \frac{25}{16}$

Factorize

$n(n + \frac{5}{4})+ \frac{5}{4}(n + \frac{5}{4})$

$(n + \frac{5}{4})(n + \frac{5}{4})$

$(n + \frac{5}{4})^2$

Hence:

$n^2 + \frac{5}{2}n + \frac{25}{16}$ = $(n + \frac{5}{4})^2$