# `6 - p^2/8 = -4` Solve the equation.

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### 2 Answers

Here's how I would solve the problem:

1) Subtract 6 from both sides

-(p^2 / 8) = -4 - 6 = -10

2) Multiply both sides by -8

p^2 = -10 * -8 = 80

3) Take the square root of both sides.

p = root 80

Now, using a little creativity (or just brute force), we can simplify this expression. 80 can also be written under the root symbol as 16 * 5. We know that 4 is the square root of 16, which means the expression can really be written as (root 4) * (5). A very important aspect of the square root of a number (while by some definitions is a purely positive concept), negative values would also for in this equation, such as -4*(root 5).

multiply the equation by 8:

48 - p^2 = -32

subtract 48 from each side:

-p^2 = -80

multiply both sides by -1:

p^2 = 80

square root both sides:

p = +- `4sqrt(5)`

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