Solve x(1+5%)^7-R=R*1-(1+5%)^-5/5%

$$x ( 1 + 5 \% ) ^ { 7 } - R = R \times \frac { 1 - ( 1 + 5 \% ) ^ { - 5 } } { 5 \% }$$

Solve for R

$$R=\frac{7355827511386641x}{27860634880000000}$$

Steps for Solving Linear Equation

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$x\left(1+\frac{1}{20}\right)^{7}-R=R\times \frac{1-\left(1+\frac{5}{100}\right)^{-5}}{\frac{5}{100}}$$

Add 1 and \frac{1}{20} to get \frac{21}{20}.

$$x\times \left(\frac{21}{20}\right)^{7}-R=R\times \frac{1-\left(1+\frac{5}{100}\right)^{-5}}{\frac{5}{100}}$$

Calculate \frac{21}{20} to the power of 7 and get \frac{1801088541}{1280000000}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{1-\left(1+\frac{5}{100}\right)^{-5}}{\frac{5}{100}}$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{1-\left(1+\frac{1}{20}\right)^{-5}}{\frac{5}{100}}$$

Add 1 and \frac{1}{20} to get \frac{21}{20}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{1-\left(\frac{21}{20}\right)^{-5}}{\frac{5}{100}}$$

Calculate \frac{21}{20} to the power of -5 and get \frac{3200000}{4084101}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{1-\frac{3200000}{4084101}}{\frac{5}{100}}$$

Subtract \frac{3200000}{4084101} from 1 to get \frac{884101}{4084101}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{\frac{884101}{4084101}}{\frac{5}{100}}$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{\frac{884101}{4084101}}{\frac{1}{20}}$$

Divide \frac{884101}{4084101} by \frac{1}{20} by multiplying \frac{884101}{4084101} by the reciprocal of \frac{1}{20}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{884101}{4084101}\times 20$$

Multiply \frac{884101}{4084101} and 20 to get \frac{17682020}{4084101}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{17682020}{4084101}$$

Subtract R\times \frac{17682020}{4084101} from both sides.

$$x\times \frac{1801088541}{1280000000}-R-R\times \frac{17682020}{4084101}=0$$

Combine -R and -R\times \frac{17682020}{4084101} to get -\frac{21766121}{4084101}R.

$$x\times \frac{1801088541}{1280000000}-\frac{21766121}{4084101}R=0$$

Subtract x\times \frac{1801088541}{1280000000} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{21766121}{4084101}R=-x\times \frac{1801088541}{1280000000}$$

Multiply -1 and \frac{1801088541}{1280000000} to get -\frac{1801088541}{1280000000}.

$$-\frac{21766121}{4084101}R=-\frac{1801088541}{1280000000}x$$

The equation is in standard form.

$$-\frac{21766121}{4084101}R=-\frac{1801088541x}{1280000000}$$

Divide both sides of the equation by -\frac{21766121}{4084101}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{21766121}{4084101}R}{-\frac{21766121}{4084101}}=-\frac{\frac{1801088541x}{1280000000}}{-\frac{21766121}{4084101}}$$

Dividing by -\frac{21766121}{4084101} undoes the multiplication by -\frac{21766121}{4084101}.

$$R=-\frac{\frac{1801088541x}{1280000000}}{-\frac{21766121}{4084101}}$$

Divide -\frac{1801088541x}{1280000000} by -\frac{21766121}{4084101} by multiplying -\frac{1801088541x}{1280000000} by the reciprocal of -\frac{21766121}{4084101}.

$$R=\frac{7355827511386641x}{27860634880000000}$$

Solve for x

$$x=\frac{27860634880000000R}{7355827511386641}$$

Steps for Solving Linear Equation

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$x\left(1+\frac{1}{20}\right)^{7}-R=R\times \frac{1-\left(1+\frac{5}{100}\right)^{-5}}{\frac{5}{100}}$$

Add 1 and \frac{1}{20} to get \frac{21}{20}.

$$x\times \left(\frac{21}{20}\right)^{7}-R=R\times \frac{1-\left(1+\frac{5}{100}\right)^{-5}}{\frac{5}{100}}$$

Calculate \frac{21}{20} to the power of 7 and get \frac{1801088541}{1280000000}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{1-\left(1+\frac{5}{100}\right)^{-5}}{\frac{5}{100}}$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{1-\left(1+\frac{1}{20}\right)^{-5}}{\frac{5}{100}}$$

Add 1 and \frac{1}{20} to get \frac{21}{20}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{1-\left(\frac{21}{20}\right)^{-5}}{\frac{5}{100}}$$

Calculate \frac{21}{20} to the power of -5 and get \frac{3200000}{4084101}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{1-\frac{3200000}{4084101}}{\frac{5}{100}}$$

Subtract \frac{3200000}{4084101} from 1 to get \frac{884101}{4084101}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{\frac{884101}{4084101}}{\frac{5}{100}}$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{\frac{884101}{4084101}}{\frac{1}{20}}$$

Divide \frac{884101}{4084101} by \frac{1}{20} by multiplying \frac{884101}{4084101} by the reciprocal of \frac{1}{20}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{884101}{4084101}\times 20$$

Multiply \frac{884101}{4084101} and 20 to get \frac{17682020}{4084101}.

$$x\times \frac{1801088541}{1280000000}-R=R\times \frac{17682020}{4084101}$$

Add R to both sides.

$$x\times \frac{1801088541}{1280000000}=R\times \frac{17682020}{4084101}+R$$

Combine R\times \frac{17682020}{4084101} and R to get \frac{21766121}{4084101}R.

$$x\times \frac{1801088541}{1280000000}=\frac{21766121}{4084101}R$$

The equation is in standard form.

$$\frac{1801088541}{1280000000}x=\frac{21766121R}{4084101}$$

Divide both sides of the equation by \frac{1801088541}{1280000000}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{1801088541}{1280000000}x}{\frac{1801088541}{1280000000}}=\frac{21766121R}{\frac{1801088541}{1280000000}\times 4084101}$$

Dividing by \frac{1801088541}{1280000000} undoes the multiplication by \frac{1801088541}{1280000000}.

$$x=\frac{21766121R}{\frac{1801088541}{1280000000}\times 4084101}$$

Divide \frac{21766121R}{4084101} by \frac{1801088541}{1280000000} by multiplying \frac{21766121R}{4084101} by the reciprocal of \frac{1801088541}{1280000000}.

$$x=\frac{27860634880000000R}{7355827511386641}$$