Question

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

Answer 1

x=1±√5

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

Answer 2

X = 1

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.