X^2-2x+13=0?

Question

factor if possible if not solve by completing the square.

Answer 1

x^2 - 2x = -13

x^2 - 2x + 1 = -12

(x-1)^2 = -12

x - 1 = sqrt -12

x = 1 +/- sqrt 12 i

Answer 2

Hello,

Factoring would have to be the numbers that multiply to be 13 and add to be -2. No such luck.

Completing the square we need to put the 13 on the other side giving us x^2 -2x = -13 now we need 1/2 of -2 then squared or (-1) squared so we have x^2 -2x +1 = -13 +1

x^2 -2x + 1 = -12 now factor giving us (x-1)^2 = -12 take the square root of both sides and we have x-1 = +/- i*sqrt(12) now add 1 to both sides giving us x = 1 +/- i sqrt(12) simplify sqrt(12) and finally we have x = 1 +/- i*2sqrt(3)

Hope This Helps!!

Answer 3

Since you can't factor, you have to complete the square by using the quadratic equation.

x = -b ± sqrt( b2-4ac ) / 2a

From problem, a = 1, b = -2, and c = 13

Your answer should be:

1 +/- 3.4641 i