Question

What is the intermediate step in the form (x+a)^2=b(x+a) 2 =b as a result of completing the square for the following equation?3x^2-18x=3x 2 −18x=\,\,357357

Answer 1

Step-by-step explanation

We must complete the square of the following polynomial:

`p(x)=3x^2-18x.`

So, we must take this polynomial to the general form:

`p(x)=(x+h)^2+k.`

1) First, we take 3 as a common factor:

`p(x)=3\cdot(x^2-6x).`

2) Now, we rewrite the expression inside the parenthesis as:

`p(x)=3\cdot(x^2-2\cdot3\cdot x).`

3) We add and subtract inside the parenthesis the number 3², so we have:

`p(x)=3\cdot(x^2-2\cdot3\cdot x+3^2-3^2)=3\cdot(x^2-2\cdot3\cdot x+3^2)-3\cdot3^2.`

4) We identify the expression inside the parenthesis as (x - 3)², then we simplify the term outside it:

`p(x)=3\cdot(x-3)^2-27.`Answer

The expression obtained after completing squares is:

`3\cdot(x-3)^2-27`