Question

Solve the quadratic equation by completing the square: x^2+2x-2=0

Answer 1

`x=√(3)-1` or
`x=-√(3)-1`

EXPLANATION

To complete the square for
`x^2+2x-2=0`.

We rewrite the equation to get

`x^2+2x=2`.

We now add
`(1)^2` to both sides to get

`x^2+2x+1^2=2+1^2`.

The expression on the Left Hand Side of the equation is a perfect square.

So our equation becomes

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

This gives us,

`(x+1)^2=3`

We take square root of both sides to obtain,

`x+1=\pm √(3)`

`x=-1\pm √(3)`

We split the
`\pm` to obtain,

`x=√(3)-1`

or

`x=-√(3)-1`

Answer 2

x = √3 - 1 and x = -√3 - 1

Explanation:

x^2 +2x - 2 = 0

To solve this equation, keep the variables on one side and constants on the other

x^2 + 2x = 2

Now to complete the square, divide the coefficient of x by 2:

2x ---> coefficient of x is 2

so 2/2 = 1

Now add the square of 1 to both the sides of the equation:

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

which makes it

(x + 1)^2 = 3

To solve it, take square root of both sides which gives

x = √3 - 1 and x = -√3 - 1