# How do you solve sqrt( 11x+3) -2x =0?

Jun 6, 2018

$x = - \frac{1}{4}$ and $x = 3$

#### Explanation:

$\sqrt{11 x + 3} - 2 x = 0$

$\sqrt{11 x + 3} = 2 x$

${\left(\sqrt{11 x + 3}\right)}^{2} = {\left(2 x\right)}^{2}$

$11 x + 3 = 4 {x}^{2}$

$0 = 4 {x}^{2} - 11 x - 3$

Factor:

$\left(4 x + 1\right) \left(x - 3\right) = 0$

$x = - \frac{1}{4}$ and $x = 3$

Jun 6, 2018

$x = \frac{13 + \sqrt{217}}{8} \mathmr{and} \frac{13 - \sqrt{217}}{8}$

#### Explanation:

$\sqrt{11 x + 3} - 2 x = 0$

Add $2 x$ to both sides;

$\sqrt{11 x + 3} - 2 x + 2 x = 0 + 2 x$

$\sqrt{11 x + 3} = 2 x$

Square both sides;

${\sqrt{11 x + 3}}^{2} = {\left(2 x\right)}^{2}$

$11 x + 3 = 4 {x}^{2}$

Rearranging the equation;

$4 {x}^{2} - 11 x - 3 = 0$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Where;

$a = 4$

$b = - 11$

$c = - 3$

Substituting the values into the equation..

$x = \frac{- \left(- 13\right) \pm \sqrt{{\left(- 13\right)}^{2} - 4 \left(4\right) \left(- 3\right)}}{2 \left(4\right)}$

$x = \frac{13 \pm \sqrt{169 + 48}}{8}$

$x = \frac{13 \pm \sqrt{217}}{8}$

$x = \frac{13 + \sqrt{217}}{8} \mathmr{and} \frac{13 - \sqrt{217}}{8}$