Solve sqrt{-9k}=sqrt{16-k}

$$\sqrt { - 9 k } = \sqrt { 16 - k }$$

Solve for k

$$k=-2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{-9k}\right)^{2}=\left(\sqrt{16-k}\right)^{2}$$

Calculate \sqrt{-9k} to the power of 2 and get -9k.

$$-9k=\left(\sqrt{16-k}\right)^{2}$$

Calculate \sqrt{16-k} to the power of 2 and get 16-k.

$$-9k=16-k$$

Add k to both sides.

$$-9k+k=16$$

Combine -9k and k to get -8k.

$$-8k=16$$

Divide both sides by -8.

$$k=\frac{16}{-8}$$

Divide 16 by -8 to get -2.

$$k=-2$$

Substitute -2 for k in the equation \sqrt{-9k}=\sqrt{16-k}.

$$\sqrt{-9\left(-2\right)}=\sqrt{16-\left(-2\right)}$$

Simplify. The value k=-2 satisfies the equation.

$$3\times 2^{\frac{1}{2}}=3\times 2^{\frac{1}{2}}$$

Equation \sqrt{-9k}=\sqrt{16-k} has a unique solution.

$$k=-2$$