Solving by completing the square(10 points.)..?

x^-2x-5=0

x^-2x=5 ...........(1)

{Using the Formula a^2-2ab+b^2=(a-b)^2}

x^2-2(x)(?)+(?)^2=5+(?)^2

It means that we have to add an unknown (?) term to both sides to complete square. In eq. (1) we have two values on the left side so we have to guess the third one. it is 1

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

Closing the left side in formula we get

(x-1)^2=5+1

(x-1)^2=6

taking sq.root to both sides we get

(x-1)= ±sq.root of 6

x=1±sq.root of 6

is the answer

x^2 - 2x + ___ = 5 + ___

Take 1/2(2) and square it, put it where the lines are.

x^2 - 2x + 1 = 5 + 1

Factor the left.

(x - 1)^2 = 6

Square root both sides.

x - 1 = +/- sqrt 6

x = +/- (sqrt 6) + 1