x^2+4x=12 by completing the square?

Question

I've been studying for a math final coming up and I'm not sure how to do this. If someone could explain it out to me, it'd be much appreciated!!!

Answer 1

x² + 4x + 4 = 12 + 4
(x + 2)² = 16
x + 2 = ± 4
x = - 2 ± 4
x = 2 , x = - 6

Answer 2

How to complete the square in general:

Add (b/2)^2 to both sides then factor the left side and solve it like you would a normal equation.

For the problem specifically:

x^2+4x + (4/2)^2=12 +(4/2)^2

(x+2)^2=16

sqareroot(x+2)^2=squareroot16

x+2=+/- 4

x=-2 +/- 4

x= -6 and 2

Answer 3

Subtract 12 from both sides.

X^2 + 4X - 12 = 0. The rest is easy.

(X - 2)(X + 6) = X^2 -2X +6X - 12
X^2 + 4X -12

X = 2 and (-6) by the way. Check: 4 + 8 - 12 = 0 O.K.
(-6)^ + 4 times (-6) - 12 = 36 + (-24) - 12 = 0 0 O.K.
This is a parabola and equations to the second degree may have two answers. Vertex (-7)

Answer 4

x^2 + 4x = 12

add 4 on both sides

x^2 + 4x + 4 = 16

(x + 2)^2 = 4^2

take square root on both sides

x + 2 = ±4

x = -2 ± 4

x = 2 or -6

Answer 5

This is a quadratic equation.
x^2+4x=12

-12 on both sides to make it equal zero.

x^2+4x-12=0
Now treat it like a trinomial.
(x+6) and (x-2)
-6 and +2
x= -6 or x=2

Answer 6

x^2+4x=12
x^2+4x - 12=0
(x+2)^2 -12 (-4)=0
(x+2)^2 -16=0
(x+2)= +-√16

Either x=2 or -6