Question

How do you solve using completing the square method `x^2 - 3x = 18`?

Answer 1

`x= -3`
`x= 6`

Explanation:

Note: The goal of completing the square is to create a perfect trinomial in the form of

`(a^2 +2ab+b^2) = (a+b)^2` `" " " or`
`(a^2 -2ab+b^2) = (a-b)^2`

Given:

`x^2 - 3x = 18`

Step 1: The leading coefficient is 1, we can proceed to the next step of completing the square

Step 2: The third term is , `[(1/2)(-3)]^2 = 9/4`

`x^2 - 3x + [(1/2)(-3)]^2 = 18 + [(1/2)(-3)]^2`

`x^2 - 3x +color(red)(9/4) = 18 + color(red)(9/4)`

Step 3: Rewrite as a perfect trinomial on the left and simplify the right side of the equation

`x^2 -3x +(3/2)^2 = 18/1 + 9/4`

`(x-3/2)^2= 72/4 +9/4`

`(x-3/2)^2 = 81/4`

Step 4: Solve the equation by taking the square root of both side
remember `sqrt(x^2) = +-x`

`sqrt((x-3/2)^2) = sqrt(81/4)`

`x-3/2 = +-9/2`

Step 5: Then solve for `x`

`x = -9/2 + 3/2` `" " or "` `x= 9/2 +3/2`

So `" " x= -6/2 = -3`

or `" " x= 12/2 = 6`