Solve a{left(1+2.2/12right)}^4=a+146.67

$$a { \left(1+ \frac{ 2.2 }{ 12 } \right) }^{ 4 } = a+146.67$$

Solve for a

$$a = \frac{1900843200}{12451681} = 152\frac{8187688}{12451681} \approx 152.657556839$$

Steps for Solving Linear Equation

Expand \frac{2.2}{12} by multiplying both numerator and the denominator by 10.

$$a\left(1+\frac{22}{120}\right)^{4}=a+146.67$$

Reduce the fraction \frac{22}{120} to lowest terms by extracting and canceling out 2.

$$a\left(1+\frac{11}{60}\right)^{4}=a+146.67$$

Add 1 and \frac{11}{60} to get \frac{71}{60}.

$$a\times \left(\frac{71}{60}\right)^{4}=a+146.67$$

Calculate \frac{71}{60} to the power of 4 and get \frac{25411681}{12960000}.

$$a\times \frac{25411681}{12960000}=a+146.67$$

Subtract a from both sides.

$$a\times \frac{25411681}{12960000}-a=146.67$$

Combine a\times \frac{25411681}{12960000} and -a to get \frac{12451681}{12960000}a.

$$\frac{12451681}{12960000}a=146.67$$

Multiply both sides by \frac{12960000}{12451681}, the reciprocal of \frac{12451681}{12960000}.

$$a=146.67\times \frac{12960000}{12451681}$$

Multiply 146.67 and \frac{12960000}{12451681} to get \frac{1900843200}{12451681}.

$$a=\frac{1900843200}{12451681}$$