Solve v^2=12^2+2x-3*18

$$v ^ { 2 } = 12 ^ { 2 } + 2 x - 3 \times 18$$

Solve for x

$$x=\frac{v^{2}-90}{2}$$

Steps for Solving Linear Equation

Calculate 12 to the power of 2 and get 144.

$$v^{2}=144+2x-3\times 18$$

Multiply 3 and 18 to get 54.

$$v^{2}=144+2x-54$$

Subtract 54 from 144 to get 90.

$$v^{2}=90+2x$$

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

$$90+2x=v^{2}$$

Subtract 90 from both sides.

$$2x=v^{2}-90$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{v^{2}-90}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{v^{2}-90}{2}$$

Divide v^{2}-90 by 2.

$$x=\frac{v^{2}}{2}-45$$

Solve for v (complex solution)

$$v=-\sqrt{2\left(x+45\right)}$$

$$v=\sqrt{2\left(x+45\right)}$$

Solve for v

$$v=\sqrt{2\left(x+45\right)}$$

$$v=-\sqrt{2\left(x+45\right)}\text{, }x\geq -45$$