Solve R=B(1-105.964/1+105.964)^2

$$R = B ( \frac { 1 - 105.964 } { 1 + 105.964 } ) ^ { 2 }$$

Solve for B

$$B=\frac{715081081R}{688590081}$$

Steps for Solving Linear Equation

Subtract 105.964 from 1 to get -104.964.

$$R=B\times \left(\frac{-104.964}{1+105.964}\right)^{2}$$

Add 1 and 105.964 to get 106.964.

$$R=B\times \left(\frac{-104.964}{106.964}\right)^{2}$$

Expand \frac{-104.964}{106.964} by multiplying both numerator and the denominator by 1000.

$$R=B\times \left(\frac{-104964}{106964}\right)^{2}$$

Reduce the fraction \frac{-104964}{106964} to lowest terms by extracting and canceling out 4.

$$R=B\left(-\frac{26241}{26741}\right)^{2}$$

Calculate -\frac{26241}{26741} to the power of 2 and get \frac{688590081}{715081081}.

$$R=B\times \frac{688590081}{715081081}$$

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

$$B\times \frac{688590081}{715081081}=R$$

The equation is in standard form.

$$\frac{688590081}{715081081}B=R$$

Divide both sides of the equation by \frac{688590081}{715081081}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{688590081}{715081081}B}{\frac{688590081}{715081081}}=\frac{R}{\frac{688590081}{715081081}}$$

Dividing by \frac{688590081}{715081081} undoes the multiplication by \frac{688590081}{715081081}.

$$B=\frac{R}{\frac{688590081}{715081081}}$$

Divide R by \frac{688590081}{715081081} by multiplying R by the reciprocal of \frac{688590081}{715081081}.

$$B=\frac{715081081R}{688590081}$$

Solve for R

$$R=\frac{688590081B}{715081081}$$

Solution Steps

Subtract 105.964 from 1 to get -104.964.

$$R=B\times \left(\frac{-104.964}{1+105.964}\right)^{2}$$

Add 1 and 105.964 to get 106.964.

$$R=B\times \left(\frac{-104.964}{106.964}\right)^{2}$$

Expand \frac{-104.964}{106.964} by multiplying both numerator and the denominator by 1000.

$$R=B\times \left(\frac{-104964}{106964}\right)^{2}$$

Reduce the fraction \frac{-104964}{106964} to lowest terms by extracting and canceling out 4.

$$R=B\left(-\frac{26241}{26741}\right)^{2}$$

Calculate -\frac{26241}{26741} to the power of 2 and get \frac{688590081}{715081081}.

$$R=B\times \frac{688590081}{715081081}$$