From second-to-last step to last step, there is an algebra error.
I have a question that requires me to solve by completing the square but leave the answers in SURD form:
I have got as far as the following:
x^2+8x+10=0
x^2+8x+10=(x-4)^2-4^2+10
(x-4)^2-16+10
(x-4)^2-6=0
(x-4)^2=6
x-4=√6 or -√6
x=4√6 or -4√6
Now I think this is wrong I just don't know what steps are missing or at what point i have made a mistake?
Any help is appreciated.
Thanks in advance.
Fortunately your starting equation is in standard form so just follow these steps:
1) Move the ten to the other side to get:
x^2 + 8x = -10
2) Take 1/2 of the number in the 8x term, square it, then add the result to both sides which yields:
x^2 + 8x + 16 = -10 + 16 = 6
3) Now factor out the left-hand side to get:
(x + 4)^2 = 6
Can you proceed from here on?