Question 280963
Stanborn was very generous in helping you.
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squared is written ^2
cubed  ^3
x^2-2x-13=0
There are three common ways to solve quadratic equations
1-factor
2-complete the square
3-quadratic formula
This one can't be factored
You can use complete the square.
SOME of your 6 steps look like it might be an attempt to complete the square.

x^2-2x-13=0
get the constant on the right
x^2-2x=13
the coeficient of x^2 must be one. It is.
take the coefficient of x not x^2
-2
take half
-2/2
square it
 1
add it to both sides
x^2-2x+1=14
(x-1)^2=14
take square root
x-1=sqrt(14)
x-1=-sqrt(14)

{{{x=1+sqrt(14)}}}
{{{x=1-sqrt(14)}}}

see below for approximate values

Quadratic formula works on ALL quadratic equations.
*[invoke quadratic "x", 1, -2, -13 ]