Solve the equation by completeing the sqaure

Question

x²-2x-2=0 is the answer to this 1 plus minus radical 3

Answer 1

Hi Sara;

x²-2x-2=0

For the FOIL...

FIRST must be (x)(x)=x²

OUTER and INNER must add-up to -2x.

(x-1)(x-1)

Let's FOIL...

FIRST...(x)(x)=x²

OUTER...(x)(-1)=-1x=-x

INNER...(-1)(x)=-1x=-x

LAST...(-1)(-1)=1

x²-x-x+1

x²-2x+1

The constant we are looking for is -2.

-2=1-3

x²-2x+1-3=0

[(x-1)(x-1)]-3=0

[(x-1)²]-3=0

(x-1)²=3

Square-root both sides...

x-1=+√3....and x-1=-√3

This is because +√3, when squared, will produce the same result as (-√3) squared...

x=1+√3.....and x=1-√3