100=5/(1+0.032)+105/(1+x)^2
You asked:
Solve the equation \(100 = \frac{5}{1 + 0.032} + \frac{105}{{\left( 1 + x \right)}^{2}}\) for the variable \(x\).
MathBot Answer:
The solutions are given by the formula: \[x = \frac{3 \left(-1\right)^{k} \sqrt{738955}}{2455} - 1\] where \(k\) is an integer in \(0 \le k < 2\).
There are \(2\) real solutions.
There are \(0\) solutions with nonzero imaginary part.
Real solutions: \[\begin{aligned}x &= -1 + \frac{3 \sqrt{738955}}{2455} \\&\approx 0.050458149\\x &= -1 - \frac{3 \sqrt{738955}}{2455} \\&\approx -2.0504581\end{aligned}\]
The are no solutions with nonzero imaginary part.