Question 1173229
start with:
x^2 - 10x + 10 = 0


subtract 10 from both sides of the equation to get:
x^2 - 10x = -10


take half the coefficient of the x term and adding it to x to get (x - 5)^2 = -10
(x - 5)^2 is equal to x^2 -10x + 25
to make (x - 5)^2 equal to x^2 - 10x, you need to subtract 25 from the result.
you get (x - 5)^2 - 25 = -10
add 25 to both sides of the equation to get:
(x - 5)^2 = 15


take the square root of both sides of this equation to get:
x - 5 = plus or minus sqrt(15)
add 5 to both sides of this equation to get:
x = 5 plus or minus sqrt(15)
that's your solution.

if you graph the equations of x^2 - 10x + 10 = y, and (x - 5)^2 - 15 = y, they should be identical.


the following graph shows that they are:


<img src = "http://theo.x10hosting.com/2021/011803.jpg" >


the roots shown are 1.127 and 8.873.
5 + sqrt(15) = 8.873 rounded to 3 decimal places.
5 - sqrt(15) = 1.127 rounded to 3 decimal places.


both equations draw the same graph.
this means they are identical.
they are two different versions of the same equation.


your solution is x = 5 plus or minus sqrt(15)