Solve 2j=3sqrt{2k+8}

$$2 j = 3 \sqrt { 2 k + 8 }$$

Solve for j (complex solution)

$$j=\frac{3\sqrt{2\left(k+4\right)}}{2}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$2j=3\sqrt{2k+8}$$

Divide both sides by 2.

$$\frac{2j}{2}=\frac{3\sqrt{2k+8}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$j=\frac{3\sqrt{2k+8}}{2}$$

Solve for j

$$j=\frac{3\sqrt{2\left(k+4\right)}}{2}$$

$$k\geq -4$$

Steps for Solving Linear Equation

The equation is in standard form.

$$2j=3\sqrt{2k+8}$$

Divide both sides by 2.

$$\frac{2j}{2}=\frac{3\sqrt{2k+8}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$j=\frac{3\sqrt{2k+8}}{2}$$

Solve for k

$$k=\frac{2\left(j^{2}-18\right)}{9}$$

$$j\geq 0$$

Steps for Solving Radical Equations

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

$$3\sqrt{2k+8}=2j$$

Divide both sides by 3.

$$\frac{3\sqrt{2k+8}}{3}=\frac{2j}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\sqrt{2k+8}=\frac{2j}{3}$$

Square both sides of the equation.

$$2k+8=\frac{4j^{2}}{9}$$

Subtract 8 from both sides of the equation.

$$2k+8-8=\frac{4j^{2}}{9}-8$$

Subtracting 8 from itself leaves 0.

$$2k=\frac{4j^{2}}{9}-8$$

Divide both sides by 2.

$$\frac{2k}{2}=\frac{\frac{4j^{2}}{9}-8}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$k=\frac{\frac{4j^{2}}{9}-8}{2}$$

Divide \frac{4j^{2}}{9}-8 by 2.

$$k=\frac{2j^{2}}{9}-4$$

Solve for k (complex solution)

$$k=\frac{2\left(j^{2}-18\right)}{9}$$

$$arg(j)<\pi \text{ or }j=0$$