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:

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

Answer 2

The perfect square form of the given expression will be $(q-\dfrac{23}{2})^2$.

The given expression is $q^2-23q$.

It is required to write the given expression as a perfect square polynomial or trinomial.

We will use the identity $(a+b)^2=a^2+2ab+b^2$.

So, the first term from the given expression will be $a=q$.

To find the second term b, divide the 2nd term of the given expression by 2,

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

So, the given expression can be written in the perfect square form as,

$a^2+2ab+b^2=q^2-23q+(\dfrac{-23}{2})^2\\=(q-\dfrac{23}{2})(q-\dfrac{23}{2})\\=(q-\dfrac{23}{2})^2$

Therefore, the perfect square form of the given expression will be $(q-\dfrac{23}{2})^2$.

For more details, refer to the link:

https://brainly.com/question/18875994