Question

Complete the square to make a perfect square trinomial. Write the result as a binomial square. q2−23q

Answer 1

Answer:

$\left(q-\dfrac{23}{2}\right)^2$

Step-by-step explanation:

Given the expression: $q^2-23q$

To complete the square, we follow these steps:

Step 1: Identify the coefficient of q

Coefficient of q=-23

Step 2: Divide the coefficient of q by 2

$=-\dfrac{23}{2}$

Step 3: Square your result from step 2 and add it to the equation

This gives us: $q^2-23q+\left(-\dfrac{23}{2}\right)^2$

We have now completed the square.

Step 4: Write the result as a binomial square.

To write it as a binomial square, pick the variable and add the term in the bracket.

Therefore:

$q^2-23q+\left(-\dfrac{23}{2}\right)^2=\left(q-\dfrac{23}{2}\right)^2$