Solve x^2+4x=20 by completing the square

x =-2 ±2 sqrt(6)

Step-by-step explanation:

x^2+4x=20

Take the coefficient of x

4

Divide by 2

4/2 =2

Then square it

2^2 =4

Add this to each side

x^2+4x +4=20+4

x^2+4x +4=24

Take the 4/2  and rewrite as (x+2)^2

(x+2)^2 = 24

Take the square root of each side

sqrt((x+2)^2) = ± sqrt(24)

x+2 =± sqrt(24)

Subtract 2 from each side

x+2-2 =-2 ± sqrt(24)

x =-2 ± sqrt(24)

We can simplify sqrt(24) as = sqrt(4*6) = 2sqrt(6)

x =-2 ±2 sqrt(6)