How do you solve sqrt(2x+1/6)=x+5/6?

Mar 21, 2017

I have taken you to a point where you can finish it off.

Explanation:

If you have a square root on one side of the equals and a 'non' square root on the other, you can 'get rid' of the root by squaring both sides. Giving:

$2 x + \frac{1}{6} = {\left(x + \frac{5}{6}\right)}^{2}$

$2 x + \frac{1}{6} = {x}^{2} + \frac{5}{3} x + \frac{25}{36}$

Collecting terms on one side only of the equals to give us a quadratic equation.

${x}^{2} + \frac{5}{3} x - 2 x + \frac{25}{36} - \frac{1}{6} = 0$

${x}^{2} - \frac{1}{3} x + \frac{19}{36} = 0$

Compare to $y = a {x}^{2} + b x + c$ where $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$\implies x = \frac{\frac{1}{3} \pm \sqrt{\left(\frac{1}{9}\right) - 4 \left(1\right) \left(\frac{19}{36}\right)}}{2 \left(1\right)}$

I will let you finish this off.