Solve 2x(x+3)=k

$$2 x ( x + 3 ) = k$$

Solve for k

$$k=2x\left(x+3\right)$$

Solution Steps

Use the distributive property to multiply 2x by x+3.

$$2x^{2}+6x=k$$

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

$$k=2x^{2}+6x$$

Solve for x (complex solution)

$$x=\frac{\sqrt{2k+9}-3}{2}$$

$$x=\frac{-\sqrt{2k+9}-3}{2}$$

Solve for x

$$x=\frac{\sqrt{2k+9}-3}{2}$$

$$x=\frac{-\sqrt{2k+9}-3}{2}\text{, }k\geq -\frac{9}{2}$$