Question

Completing the Square of

x2-10x+22=-2

Answer 1

start with
\[x^2-10x=-24\] then take halve of -10 and square it to get
\[(x-5)^2=-24+5^2=-24+25=1\]

Answer 2

once you have
\[(x-5)^2=1\] you know
\[x-5=1\text { or } x-5=-1\] so
\[x=6\text{ or } x=4\]

Answer 3

x^2-10 x+22 = -2
Subtract 22 from both sides:
x^2-10 x = -24
Add 25 to both sides:
x^2-10 x+25 = 1
Factor the left hand side:
(x-5)^2 = 1
Take the square root of both sides:
sqrt(x-5) = 1
Eliminate the absolute value:
x-5 = -1 or x-5 = 1
Add 5 to both sides:
x = 4 or x-5 = 1
Add 5 to both sides:
x = 4 or x = 6

Answer 4

thank you (: