Question

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

Answer 1

ANSWER

$x=\sqrt{3}-1$ or $x=-\sqrt{3}-1$

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,

$x+1=\pm \sqrt{3}$

$x=-1\pm \sqrt{3}$

We split the $\pm$ to obtain,

$x=\sqrt{3}-1$

or

$x=-\sqrt{3}-1$

Answer 2

Answer:

x = √3 - 1 and x = -√3 - 1

Step-by-step 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