Question

How do you solve `x^2 + 2x = 3` by completing the square?

Answer 1

Add the square of half the coefficient of `x` to both sides; take the square root of both sides and perform standard arithmetic operations to get: `x = -3 or +1`

Explanation:

Given `x^2+2x=3`

Add the square of (`1/2` of `2`)
`color(white)("XXXX")` `x^2+2x+1 = 3+1`

Rewrite the left side as a binomial square (and simplify the right side)
`color(white)("XXXX")` `(x+1)^2 = 4`

Take the square root of both sides
`color(white)("XXXX")` `x+1 = +-2`

Subtract `1` from both sides
`color(white)("XXXX")` `x= -3 or +1`