Sole by completing the square

solve x squared-6x-13=0 by completing the square

x² - 6x - 13 + 13 = 0 + 13
.. x² - 6x = 13

since x² - 2(x)(b) + b² = (x + b)², so
x² - 6x + (-6/2)² = 13 + (-6/2)²
(x - 3)² = 13 + 9 = 22
√(x - 3)² = ±√(22)
x - 3 = ±√22
x = 3±√22

{3±√22}

Okay, so your A-term is 1. Now, we have to move the -13 to the other side

x^2-6x-13=0
+13 +13
x^2-6x+_=13+_ Now we divide our b-term by 2 and square the quotient.
(-6/2)^2=(-3)^2=9
x^2-6x+9=13+9 =>x^2-6x+9=21 Now, we factor the trinomial.
(x-3)(x-3)=21 => (x-3)^2=21 Now, we solve for x
x-3=21
+3 +3
x=24

x^2 - 6x - 13 = 0
(x - 3)^2 - 9 - 13 = 0
(x - 3)^2 = 22
x - 3 = +/- Sqrt22
x = 3 + Sqrt22
and
x = 3 - Sqrt22
if you need to go further
x = 3 + 4.69 = 7.69
x = 3 - 4.69 = - 1.69

x² - 6x - 13 = 0

x² - 6x = 13

x² - 6x + (-3)² = 13 + 9

(x - 3)² = 22

x - 3 = ±√(22)

x = 3 ± √(22)