Question

How do you solve using the completing the square method `2x^2+3x=20`?

Answer 1

`x = 2 1/2 " or " x = -4`

Explanation:

Completing the square is based on the fact that when a binomial is squared, there is a specific relationship between the coefficients of the 2nd and 3rd terms."

`(x - 5)^2 = x^2 - 10x + 25`
Note that (-10) divided by 2 and then squared gives 25.

We have `2x^2 + 3x = 20" divide by 2 first to get " x^2`

`x^2 + 3/2 x " " = 10" "` `(3/2)÷ 2 = (3/4)`

Add `(3/4)^2` to both sides
`x^2 + 3/2 x + color(red)((3/4)^2) = 10 + color(red)((3/4)^2)`
The left side can now be written as `"(binomial)"^2`

`(x + 3/4)^2 " " = 169/16`

`x + 3/4 = +-(13/4)" find the square root of both sides"`

`x = 13/4 - 3/4 " or "x = -13/4 - 3/4`

`x = 10/4 " or " x = -16/4`

`x = 2 1/2 " or "x = -4`