Question

How do you solve `w ^ { 2} + 4m = 45`?

Answer 1

`w = +- sqrt(45 - 4m)`
`m = (45- w^2) // 4`

Explanation:

With a some rearranging you can express `w` in function of `m` and `m` in function of `w`

Solve for `w` :

`w^2 + 4m = 45`

Subtract `4m` to both sides
`w^2 + cancel(4m - 4m) = 45 - 4m`

Take the square root of both sides
`sqrt(w^2) = +- sqrt(45 - 4m)`

We know that `AA x; sqrt(x^2) = x`
`w = +- sqrt(45 - 4m)`

Solve for `m` :

`w^2 + 4m = 45`

Subtract `w^2` to both sides
`cancel(w^2 - w^2) + 4m = 45 - w^2`

Divide both sides by `4`
`cancel(4)m // cancel(4) = (45 - w^2) // 4`

Write correctly the equation
`m = (45- w^2) // 4`