When I have:
-(x + 1)^2 = 4
Do I take the square root of -(x + 1) or (x + 1)?
Also, am I doing this question properly?
Ohhh...do when there is an equation and for example I have to subtract something from both sides but also multiply both sides, I have to subtract the number first before dividing the equation with the other number?
(2 + 3) / 3 = x + 1
Do I have to subtract 3 from both sides first? And them multiply by the 3 on both sides after that?
Think of it this way- when you are giving someone a birthday present, you must (1) put the present in a box, (2) close the box, (3) wrap with gift paper, and (4) tie the bow.
If you receive the present, you must do the opposite of each step, in the opposite order, (1) untie the bow, (2) unwrap the paper, (3) open the box, (4) remove the present.
It is the same way with solving algebraic equations. If you were given the formula $\displaystyle -(x- 1)^2/4$, a value of x, and asked for the value of the function, you would (1) subtract 1 from x, (2) square that result, (3)multiply by -1, (4) divide by 4. If, however, you are given a value of the formula, and asked to find x, you do the opposite of each step, in the opposite order. That is, (1) multiply by 4, (2) divide by -1, (3) take the square root, (4) add 1.
Now, it is not always possible to "reverse" every operation. Here, if we are given that the formula is equal to 1, that is given $\displaystyle \frac{-(x+1)^2}{4}= 1$. Multiplying both sides by 4, we have $\displaystyle -(x+1)^2= 4$, dividing by -1, $\displaystyle (x+1)^2= -4$. Now, as long as we stay in the real number system, there is no number whose square is -4 so we cannot take the square root.
If, however, we are working in the complex number system, both 2i and -2i have the property that their square is -4. So we can write $\displaystyle x+ 1= 2i$ and $\displaystyle x+ 1= -2i$. Then, of course, the last step would be to subtract 2 from both sides, leaving $\displaystyle x= -1+ 2i$ and $\displaystyle x= -1- 2i$.