Question

Complete the square to solve 4x2 + 24x = 4?

Answer 1

`x=0.1623, -6.1623`

Explanation:

nothing can be in the `a` spot to complete the square so divide everything by `4`
`x^2+6x=1`
Divide `b` term by `2` then square it:
`(6/2)^2=9`
add to both sides:
`x^2+6x+9=10`
Now factor
Tip the factor is ALWAYS going to be the `b` term divided by `2` in this case that is `3`
`(x+3)^2=10`
Square root both sides to get `x` alone
`x+3=+-√10`
`x=-3+-√10`
`x=0.1623, -6.1623`

Answer 2

`x= -3+-sqrt(10)`

Explanation:

`4x^2+24x= 4`

1. Factor out the `4`
   `4(x^2+6x)= 4`

2. Complete the square with `(b/2)^2` and add the same to the other side of the equal to sign:
   `4(x^2+6x+9)= 4+36`

3. Factor
   `4(x+3)^2= 40`

4. Simplify
   `(x+3)^2= 10`

`x+3= +-sqrt(10)`

`x= -3+-sqrt(10)`