solve equation x $\sqrt{5}$ + 32 = x $\sqrt{45}$ +2x
You asked:
Solve the equation \[\sqrt{5} + 32 = x \cdot \sqrt{45} + 2 x\] for the unknown \(x\).
MathBot Answer:
The solution is: \[x = - \frac{49}{41} + \frac{94 \sqrt{5}}{41} \approx 3.9314729\]
\[\begin{aligned}\sqrt{5} + 32 &= x \left(2 + 3 \sqrt{5}\right)\\x \left(- 3 \sqrt{5} - 2\right) &= -32 - \sqrt{5}\\x &= \frac{-32 - \sqrt{5}}{- 3 \sqrt{5} - 2}\end{aligned}\]