Solve f^22v+2/8=v-7/4-v

$$f ^ { 2 } \frac { 2 v + 2 } { 8 } = \frac { v - 7 } { 4 } - v$$

Solve for v (complex solution)

$$v=-\frac{f^{2}+7}{f^{2}+3}$$

$$f\neq -\sqrt{3}i\text{ and }f\neq \sqrt{3}i$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 8,4.

$$f^{2}\left(2v+2\right)=2\left(v-7\right)-8v$$

Use the distributive property to multiply f^{2} by 2v+2.

$$2f^{2}v+2f^{2}=2\left(v-7\right)-8v$$

Use the distributive property to multiply 2 by v-7.

$$2f^{2}v+2f^{2}=2v-14-8v$$

Combine 2v and -8v to get -6v.

$$2f^{2}v+2f^{2}=-6v-14$$

Add 6v to both sides.

$$2f^{2}v+2f^{2}+6v=-14$$

Subtract 2f^{2} from both sides.

$$2f^{2}v+6v=-14-2f^{2}$$

Combine all terms containing v.

$$\left(2f^{2}+6\right)v=-14-2f^{2}$$

The equation is in standard form.

$$\left(2f^{2}+6\right)v=-2f^{2}-14$$

Divide both sides by 2f^{2}+6.

$$\frac{\left(2f^{2}+6\right)v}{2f^{2}+6}=\frac{-2f^{2}-14}{2f^{2}+6}$$

Dividing by 2f^{2}+6 undoes the multiplication by 2f^{2}+6.

$$v=\frac{-2f^{2}-14}{2f^{2}+6}$$

Divide -14-2f^{2} by 2f^{2}+6.

$$v=-\frac{f^{2}+7}{f^{2}+3}$$

Solve for v

$$v=-\frac{f^{2}+7}{f^{2}+3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 8,4.

$$f^{2}\left(2v+2\right)=2\left(v-7\right)-8v$$

Use the distributive property to multiply f^{2} by 2v+2.

$$2f^{2}v+2f^{2}=2\left(v-7\right)-8v$$

Use the distributive property to multiply 2 by v-7.

$$2f^{2}v+2f^{2}=2v-14-8v$$

Combine 2v and -8v to get -6v.

$$2f^{2}v+2f^{2}=-6v-14$$

Add 6v to both sides.

$$2f^{2}v+2f^{2}+6v=-14$$

Subtract 2f^{2} from both sides.

$$2f^{2}v+6v=-14-2f^{2}$$

Combine all terms containing v.

$$\left(2f^{2}+6\right)v=-14-2f^{2}$$

The equation is in standard form.

$$\left(2f^{2}+6\right)v=-2f^{2}-14$$

Divide both sides by 2f^{2}+6.

$$\frac{\left(2f^{2}+6\right)v}{2f^{2}+6}=\frac{-2f^{2}-14}{2f^{2}+6}$$

Dividing by 2f^{2}+6 undoes the multiplication by 2f^{2}+6.

$$v=\frac{-2f^{2}-14}{2f^{2}+6}$$

Divide -14-2f^{2} by 2f^{2}+6.

$$v=-\frac{f^{2}+7}{f^{2}+3}$$

Solve for f (complex solution)

$$f=-i\left(v+1\right)^{-\frac{1}{2}}\sqrt{3v+7}$$

$$f=i\left(v+1\right)^{-\frac{1}{2}}\sqrt{3v+7}\text{, }v\neq -1$$

Solve for f

$$f=\sqrt{-\frac{3v+7}{v+1}}$$

$$f=-\sqrt{-\frac{3v+7}{v+1}}\text{, }v\geq -\frac{7}{3}\text{ and }v<-1$$