Question

How do you solve `sqrt(9u-4)=sqrt(7u-20)`?

Answer 1

See a solution process below:

Explanation:

First, square both sides of the equation to eliminate the radicals while keeping the equation balanced:

`(sqrt(9u - 4))^2 = (sqrt(7u - 20))^2`

`9u - 4 = 7u - 20`

Next, add `color(red)(4)` and subtract `color(blue)(7u)` from each side of the equation to isolate the `u` term while keeping the equation balanced:

`9u - color(blue)(7u) - 4 + color(red)(4) = 7u - color(blue)(7u) - 20 + color(red)(4)`

`(9 - color(blue)(7))u - 0 = 0 - 16`

`2u = -16`

Now, divide each side of the equation by `color(red)(2)` to solve for `u` while keeping the equation balanced:

`(2u)/color(red)(2) = -16/color(red)(2)`

`(color(red)(cancel(color(black)(2)))u)/cancel(color(red)(2)) = -8`

`u = -8`

Answer 2

See below.

Explanation:

`sqrt(9u-4)=sqrt(7u-20)`

Start by squaring both sides. This will remove the radicals:

`(sqrt(9u-4))^2=(sqrt(7u-20))^2`

`9u-4=7u-20`

Collect all terms containing the variable on one side of the equation, and all constant terms on the opposite side:

`9u-7u=-20+4`

Simplify by adding like terms:

`2u=-16`

We need to get a `u` on its own.

Divide both sides by `2`:

`(2u)/2=(-16)/2->(cancel(2)u)/cancel(2)=(-cancel(16)8)/cancel(2)->color(blue)(u=-8)`