Question

2^(2x+1) - 21* 2^(2x+3) + 2 >=0

Answer 1

  $2^{2x+1}-21\cdot 2^{2x+3}+2 \geq 0\\\\2^{2x}\cdot 2-21\cdot 2^{2x}\cdot 2^3+2 \geq 0\\\\2^{2x}(2-168) \geq -2\\\\2^{2x} \leq \frac{2}{166}\; ,\; \; 2^{2x} \leq \frac{1}{83}\; ,\; \; 2^{2x} \leq 2^{log_2{\frac{1}{83}}}\\\\2x \leq log_2{\frac{1}{83}}\; ,\; \; x \leq \frac{1}{2}\cdot log_2(83^{-1})\; ,\; \; x \leq -\frac{\log_2{83}}{2}$