Solve 515=0.2*1.05*10^2(0.1-v_{2})

$$515 = 0.2 * 1.05 \times 10 ^ { 2 } ( 0.1 - v _ { 2 } )$$

Solve for v_2

$$v_{2} = -\frac{5129}{210} = -24\frac{89}{210} \approx -24.423809524$$

Steps for Solving Linear Equation

Multiply 0.2 and 1.05 to get 0.21.

$$515=0.21\times 10^{2}\left(0.1-v_{2}\right)$$

Calculate 10 to the power of 2 and get 100.

$$515=0.21\times 100\left(0.1-v_{2}\right)$$

Multiply 0.21 and 100 to get 21.

$$515=21\left(0.1-v_{2}\right)$$

Use the distributive property to multiply 21 by 0.1-v_{2}.

$$515=2.1-21v_{2}$$

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

$$2.1-21v_{2}=515$$

Subtract 2.1 from both sides.

$$-21v_{2}=515-2.1$$

Subtract 2.1 from 515 to get 512.9.

$$-21v_{2}=512.9$$

Divide both sides by -21.

$$v_{2}=\frac{512.9}{-21}$$

Expand \frac{512.9}{-21} by multiplying both numerator and the denominator by 10.

$$v_{2}=\frac{5129}{-210}$$

Fraction \frac{5129}{-210} can be rewritten as -\frac{5129}{210} by extracting the negative sign.

$$v_{2}=-\frac{5129}{210}$$