Thread: Completing the square confusing me

1. Completing the square confusing me

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.

2. From second-to-last step to last step, there is an algebra error.

3. Thanks for the quick reply, much appreciated. that's where I thought the error was but I thought you square root each side.

Again many thanks.

4. Nope, everything's good up to that last step. What should you be doing there?

5. Actually, I'm wrong. Look here:

$\displaystyle x^{2}+8x+10=0$
$\displaystyle x^{2}+8x+16-16+10=0$
$\displaystyle (x+4)^{2}-6=0$
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.
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6. $\displaystyle x^2+8x+10=0$
$\displaystyle x^2+8x+10+6 = 6 \Rightarrow (x+4)^2-6=0$
$\displaystyle x = -4\pm\sqrt{6}$

EDIT: to late again...

7. Thanks a lot!

8. Another way of going about it

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?