Solve 5^prime=V(120)^2-(120)(-80)+(-80)^2+3(50)^2

$$5 ^ { \prime } = V ( 120 ) ^ { 2 } - ( 120 ) ( - 80 ) + ( - 80 ) ^ { 2 } + 3 ( 50 ) ^ { 2 }$$

Solve for V

$$V = -\frac{235}{144} = -1\frac{91}{144} \approx -1.631944444$$

Steps for Solving Linear Equation

Calculate 120 to the power of 2 and get 14400.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5)=V\times 14400-120\left(-80\right)+\left(-80\right)^{2}+3\times 50^{2}$$

Multiply 120 and -80 to get -9600.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5)=V\times 14400-\left(-9600\right)+\left(-80\right)^{2}+3\times 50^{2}$$

The opposite of -9600 is 9600.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5)=V\times 14400+9600+\left(-80\right)^{2}+3\times 50^{2}$$

Calculate -80 to the power of 2 and get 6400.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5)=V\times 14400+9600+6400+3\times 50^{2}$$

Add 9600 and 6400 to get 16000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5)=V\times 14400+16000+3\times 50^{2}$$

Calculate 50 to the power of 2 and get 2500.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5)=V\times 14400+16000+3\times 2500$$

Multiply 3 and 2500 to get 7500.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5)=V\times 14400+16000+7500$$

Add 16000 and 7500 to get 23500.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5)=V\times 14400+23500$$

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

$$V\times 14400+23500=\frac{\mathrm{d}}{\mathrm{d}x}(5)$$

Subtract 23500 from both sides.

$$V\times 14400=\frac{\mathrm{d}}{\mathrm{d}x}(5)-23500$$

The equation is in standard form.

$$14400V=-23500$$

Divide both sides by 14400.

$$\frac{14400V}{14400}=-\frac{23500}{14400}$$

Dividing by 14400 undoes the multiplication by 14400.

$$V=-\frac{23500}{14400}$$

Reduce the fraction \frac{-23500}{14400} to lowest terms by extracting and canceling out 100.

$$V=-\frac{235}{144}$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

$$V = -\frac{235}{144} = -1\frac{91}{144} = -1.6319444444444444$$

Solve for x

$$x\in \mathrm{R}$$

$$V = -\frac{235}{144} = -1\frac{91}{144} = -1.6319444444444444$$