Solve sqrt{-12-2n}=sqrt{-4-n}

$$\sqrt { - 12 - 2 n } = \sqrt { - 4 - n }$$

Solve for n

$$n=-8$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{-12-2n}\right)^{2}=\left(\sqrt{-4-n}\right)^{2}$$

Calculate \sqrt{-12-2n} to the power of 2 and get -12-2n.

$$-12-2n=\left(\sqrt{-4-n}\right)^{2}$$

Calculate \sqrt{-4-n} to the power of 2 and get -4-n.

$$-12-2n=-4-n$$

Add n to both sides.

$$-12-2n+n=-4$$

Combine -2n and n to get -n.

$$-12-n=-4$$

Add 12 to both sides.

$$-n=-4+12$$

Add -4 and 12 to get 8.

$$-n=8$$

Multiply both sides by -1.

$$n=-8$$

Substitute -8 for n in the equation \sqrt{-12-2n}=\sqrt{-4-n}.

$$\sqrt{-12-2\left(-8\right)}=\sqrt{-4-\left(-8\right)}$$

Simplify. The value n=-8 satisfies the equation.

$$2=2$$

Equation \sqrt{-2n-12}=\sqrt{-n-4} has a unique solution.

$$n=-8$$