Solve -sqrt{6}=4-sqrt{a}

$$- \sqrt { 6 } = 4 - \sqrt { a }$$

Solve for a

$$a=8\sqrt{6}+22\approx 41.595917942$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$4-\sqrt{a}=-\sqrt{6}$$

Subtract 4 from both sides.

$$-\sqrt{a}=-\sqrt{6}-4$$

Divide both sides by -1.

$$\frac{-\sqrt{a}}{-1}=\frac{-\sqrt{6}-4}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{a}=\frac{-\sqrt{6}-4}{-1}$$

Divide -\sqrt{6}-4 by -1.

$$\sqrt{a}=\sqrt{6}+4$$

Square both sides of the equation.

$$a=8\sqrt{6}+22$$