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

2 Answers
Apr 16, 2018

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

Apr 16, 2018

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)