Solve a{left(1+22/12right)}^4=a+14667

$$a { \left(1+ \frac{ 22 }{ 12 } \right) }^{ 4 } = a+14667$$

Solve for a

$$a = \frac{19008432}{82225} = 231\frac{14457}{82225} \approx 231.175822438$$

Steps for Solving Linear Equation

Reduce the fraction \frac{22}{12} to lowest terms by extracting and canceling out 2.

$$a\left(1+\frac{11}{6}\right)^{4}=a+14667$$

Add 1 and \frac{11}{6} to get \frac{17}{6}.

$$a\times \left(\frac{17}{6}\right)^{4}=a+14667$$

Calculate \frac{17}{6} to the power of 4 and get \frac{83521}{1296}.

$$a\times \frac{83521}{1296}=a+14667$$

Subtract a from both sides.

$$a\times \frac{83521}{1296}-a=14667$$

Combine a\times \frac{83521}{1296} and -a to get \frac{82225}{1296}a.

$$\frac{82225}{1296}a=14667$$

Multiply both sides by \frac{1296}{82225}, the reciprocal of \frac{82225}{1296}.

$$a=14667\times \frac{1296}{82225}$$

Multiply 14667 and \frac{1296}{82225} to get \frac{19008432}{82225}.

$$a=\frac{19008432}{82225}$$