Question

Solve x2 + 2x = 4 for x by completing the square. x equals plus or minus square root of 5 plus 1 x equals plus or minus square root of 5 minus 1 x = 1 x = 3

Answer 1

x equals plus or minus square root of 5 minus 1

Explanation:

we have

`x^(2) +2x=4`

Divide by 2 the coefficient of the x-term

`2/2=1`

squared the number

`1^2=1`

Adds both sides

`x^(2) +2x+1=4+1`

`x^(2) +2x+1=5`

Rewrite as perfect squares

`(x+1)^(2)=5`

take the square root both sides

`x+1=(+/-)√(5)`

`x=(+/-)√(5)-1`

therefore

x equals plus or minus square root of 5 minus 1