Question

How do you solve `\sqrt { 2x + 1} - \sqrt { 4x } = 0`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(sqrt(4x))` to both sides of the equation:

`sqrt(2x + 1) - sqrt(4x) + color(red)(sqrt(4x)) = 0 + color(red)(sqrt(4x))`

`sqrt(2x + 1) - 0 = color(red)(sqrt(4x))`

`sqrt(2x + 1) = sqrt(4x)`

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

`(sqrt(2x + 1))^2 = (sqrt(4x))^2`

`2x + 1 = 4x`

Then, subtract `color(red)(2x)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(red)(2x) + 2x + 1 = -color(red)(2x) + 4x`

`0 + 1 = (-color(red)(2) + 4)x`

`1 = 2x`

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

`1/color(red)(2) = (2x)/color(red)(2)`

`1/2 = (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2))`

`1/2 = x`

`x = 1/2`

Or

`x = 0.5`