Question

How do you solve `3+36p^2=103`?

Answer 1

Collect like terms and move the numbers until the equation reads `p^2=...` Then, take the square root of both sides of the equation.

Explanation:

Here it is:

`36p^2 = 103 -3` (we subtract 3 from each side)

`36p^2=100`

Next, divide each side by 36

`p^2=100/36`

(Resist the temptation to convert to decimals at this stage. It is actually easier with fractions!)

Square root:

`p=sqrt(100/36) = (sqrt100)/(sqrt36) = +-10/6 = +-5/3`

So, we have two answers (as expected!)

`5/3` and `-5/3`

Answer 2

See the entire solution process below:

Explanation:

First, subtract `color(red)(3)` from each side of the equation to isolate the `p^2` term while keeping the equation balanced:

`-color(red)(3) + 3 + 36p^2 = -color(red)(3) + 103`

`0 + 36p^2 = 100`

`36p^2 = 100`

Next, divide each side of the equation by `color(red)(36)` to isolate `p^2` while keeping the equation balanced:

`(36p^2)/color(red)(36) = 100/color(red)(36)`

`p^2 = 100/36`

Now, take the square root of each side of the equation to solve for `p` while keeping the equation balanced. Remember, when taking the square root of a number there is a negative and positive result:

`sqrt(p^2) = +-sqrt(100/36)`

`p = +-sqrt(100)/sqrt(36)`

`p = +-10/6`

`p = +-5/3`