Question

How do you solve `7p^2+16=2151`?

Answer 1

`+-17.5`

Explanation:

First rearrange the equation to have all like terms on one side and unlike terms on the other:

`7p^2 = 2135`

Divide by `7` to get `p` on its own and then square root it.

`p^2 = 305`
`sqrt(p^2)= +-sqrt(305)`

`p =+-sqrt(305)`

`= +-17.4642492`

`= +-17.5` (to 3 sf)

Answer 2

See a solution process below:

Explanation:

First, subtract `color(red)(16)` from each side of the equation to isolate the `p` term while keeping the equation balanced:

`7p^2 + 16 - color(red)(16) = 2151 - color(red)(16)`

`7p^2 + 0 = 2135`

`7p^2 = 2135`

Next, divide each side of the equation by `color(red)(7)` to isolate `p^2` while keeping the equation balanced:

`(7p^2)/color(red)(7) = 2135/color(red)(7)`

`(color(red)(cancel(color(black)(7)))p^2)/cancel(color(red)(7)) = 305`

`p^2 = 305`

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

`sqrt(p^2) = +-sqrt(305)`

`p = +-17.464` rounded to the nearest thousandth.