Question

Justify each step of the proof.

Conjecture: If 2(x2 + 5) = 60, then x is 5 or –5.

1. 2(x2 + 5) = 601. Given

2. 2x2 + 10 = 602.Distrubutive law

3. 2x2 = 503. Equals subtracted from equal, remainders are equal.

4. x2 = 254. Equals divided by equals quotients are equal.

5. x = ±55. Square roots of equals are equal.

Answer 1

I assume that the x is squared
(on Yahoo!Answers, we often use the caret ^ to show a power or an exponent)
(think of it as a tiny arrow pointing up, showing that the following number should be seen as if it were raised above the line)

2(x^2 + 5) = 60

Can it be x = 5 ?
we test:
2(5^2 + 5) = 2(25 + 5) = 2(30) = 60
it works, therefore x = 5 is a solution.

Can it be x = -5?
we test again:
2[(-5)^2 + 5) = 2(25 + 5) = 2(30) = 60
it works, therefore x = -5 is also a solution.

The way you did it, there could be some confusion between step 4 and step 5 (because you do not explain how you go from 4 to 5).
If you simply "take the square root" on both sides, someone could argue that the "principal" square root of a number is the positive value (+5 only, not -5). On the other hand, if you state:
(after step 4), we look for all values that give 25 when they are squared, then -5 is allowed.

The way the conjecture is stated at the beginning, the easiest way is to check both values to find out that, yes, they are both valid solutions.