Question

How do you solve `n^2 - 17=64` using the quadratic formula?

Answer 1

`n=+-9`

Explanation:

`n^2-17=64`
`n^2=64+17`
`n^2=81`
`n=sqrt81`
`n=+-9`

Answer 2

`n=+-9`

Explanation:

Write as `n^2-81`

As it is insisted we use the quadratic formula write as:

`n^2+0n-81=0`

`=>n=(-0+-sqrt(0^2-4(1)(-81)))/(2(1))`

`=>n=+-sqrt(324)/2=(+-18)/2 = +-9`

Answer 3

`n=9, -9`

Explanation:

`n^2-17=64`

Subtract `64` from both sides of the equation.

`n^2-17-64=0`

Simplify.

`n^2-81`

This equation is in the form of a quadratic equation, `ax^2+bx+c=0`, where `a=1`, `b=0`, and `c=-81`.

The quadratic formula can be used to solve this quadratic equation.

`x=(-b^2+-sqrt(b^2-4ac))/(2a)`

Substitute `n` for `x` and plug the known values into the formula.

`n=(-0+-sqrt(0^2-4*1*-81))/(2*1)`

Simplify.

`n=(+-sqrt(324))/(2)`

Simplify.

`n=+-18/2`

Simplify.

`n=+-9`

Solve for `n`.

`n=9`

`n=-9`