Question

How do you solve `(8sqrt( 2x-1)) / 3 = x`?

Answer 1

First, send the 3 to the other side in multiplication.

Explanation:

`8(sqrt(2x - 1)) = 3x`

`sqrt(2x - 1) = 3/8x`

Get rid of the square root by squaring both sides of the equation.

`(sqrt(2x - 1))^2 = (3/8x)^2`

`2x - 1 = 9/64x^2`

`64(2x - 1) = 9x^2`

`128x - 64 = 9x^2`

Solving by completing the square:

`-64 = 9(x^2 + 128/9 + m - m)`

`m = (b/2)^2`

`m = ((128/9)/2)^2`

`m = 16384/324`

`-64 = 9(x^2 + 128/9 + 16384/324 - 16384/324)`

`-64 = 9(x^2 + 128/9 + 16384/324) - 147456/324`

`(-64 + 147456/324)/9 = (x + 128/18)^2`

`126720/2916 = (x + 128/18)^2`

`+-sqrt(126720/2915) - 128/18 = x`

`-0.52 ~= x and -13.70 ~= x`

When you plug both these answers into the original equation, they both make the square root negative inside. This means there is no solution

Hopefully this helps!