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

Feb 16, 2016

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

#### Explanation:

$8 \left(\sqrt{2 x - 1}\right) = 3 x$

$\sqrt{2 x - 1} = \frac{3}{8} x$

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

${\left(\sqrt{2 x - 1}\right)}^{2} = {\left(\frac{3}{8} x\right)}^{2}$

$2 x - 1 = \frac{9}{64} {x}^{2}$

$64 \left(2 x - 1\right) = 9 {x}^{2}$

$128 x - 64 = 9 {x}^{2}$

Solving by completing the square:

$- 64 = 9 \left({x}^{2} + \frac{128}{9} + m - m\right)$

$m = {\left(\frac{b}{2}\right)}^{2}$

$m = {\left(\frac{\frac{128}{9}}{2}\right)}^{2}$

$m = \frac{16384}{324}$

$- 64 = 9 \left({x}^{2} + \frac{128}{9} + \frac{16384}{324} - \frac{16384}{324}\right)$

$- 64 = 9 \left({x}^{2} + \frac{128}{9} + \frac{16384}{324}\right) - \frac{147456}{324}$

$\frac{- 64 + \frac{147456}{324}}{9} = {\left(x + \frac{128}{18}\right)}^{2}$

$\frac{126720}{2916} = {\left(x + \frac{128}{18}\right)}^{2}$

$\pm \sqrt{\frac{126720}{2915}} - \frac{128}{18} = x$

$- 0.52 \cong x \mathmr{and} - 13.70 \cong x$

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!