How do you solve - d = 3 sqrt (d - 2)?

Mar 7, 2016

You must first isolate the square root.

Explanation:

$- d = 3 \sqrt{d - 2}$

$- \frac{d}{3} = \sqrt{d - 2}$

You must square both sides of the equation to get rid of the equation.

${\left(- \frac{d}{3}\right)}^{2} = {\left(\sqrt{d - 2}\right)}^{2}$

${d}^{2} / 9 = d - 2$

${d}^{2} = 9 \left(d - 2\right)$

${d}^{2} = 9 d - 18$

${d}^{2} - 9 d + 18 = 0$

$\left(d - 6\right) \left(d - 3\right) = 0$

$d = 6 \mathmr{and} d = 3$

Check your solutions back in the equation. Neither work, so there is no solution. Therefore, the solution is $\left\{\emptyset\right\}$.

Practice exercises:

Solve for x:

a) $\sqrt{2 x + 1} = \sqrt{4 x} - 1$

b). $\sqrt{2 x + 2} + \sqrt{9 x - 2} = 12$

Challenge problem

Solve the following system.

$\sqrt{8 x + 1} + \sqrt{y + 4} = 3 x - 1$
$\sqrt{11 x + 3} - \sqrt{y - 1} = x + 1$

Good luck!