Solve x2 + 2x = 4 for x by completing the square.

X = 1

Step-by-step explanation:

We know that 4 is the answer to the equation, as it is listed behind the "="

If we take the variable "x" out of the equation then we get something much simpler:

2 + 2 = 4

This makes sense, right?

So how do the variables squeeze into the situation?

Well, if you substitute the variable "x" for, say, another "2", then this is what we would have:

2 x 2 + 2 x 2 = 4

This one doesn't make sense, because if we simplified it, the answer would be 8, not 4!

If we substitute the "x" for 1

2 x 1 + 2 x 1 = 4

Then when worked out the problem makes sense, because any number times 1 is the same, and the answer woulld still be 4!

Thus, 1 is the answer.

x=1±√5

Step-by-step explanation:

using the method of completing the square

∙ the coefficient of the x2 term must be 1 which it is

∙ add/subtract (12coefficient of x-term) 2 to

x2-2x

⇒x2+2 (-1) x+1-1-4=0

⇒ (x-1) 2-5=0←add 5 to both sides

⇒ (x-1) 2=5

Take square root of both sides

⇒x-1=±√5←note plus or minus

add 1 to both sides

⇒x=1±√5←exact solutions

using the method of completing the square

∙ the coefficient of the x2 term must be 1 which it is

∙ add/subtract (12coefficient of x-term) 2 to

x2-2x

⇒x2+2 (-1) x+1-1-4=0

⇒ (x-1) 2-5=0←add 5 to both sides

⇒ (x-1) 2=5

Take square root of both sides

⇒x-1=±√5←note plus or minus

add 1 to both sides

⇒x=1±√5←exact solutions