Question

How do you solve the equation `x^2+3x-18=0` by completing the square?

Answer 1

`x = 3" "` or `" "x=-6`

Explanation:

The difference of squares identity can be written:

`a^2-b^2 = (a-b)(a+b)`

Use this with `a=(2x+3)` and `b=9` as follows:

`0 = 4(x^2+3x-18)`

`color(white)(0) = 4x^2+12x-72`

`color(white)(0) = (2x)^2+2(2x)(3)+9-81`

`color(white)(0) = (2x+3)^2-9^2`

`color(white)(0) = ((2x+3)-9)((2x+3)+9)`

`color(white)(0) = (2x-6)(2x+12)`

`color(white)(0) = (2(x-3))(2(x+6))`

`color(white)(0) = 4(x-3)(x+6)`

Hence:

`x = 3" "` or `" "x=-6`