Question

Radical din 16x + x pătrat = 11 - 2x

Answer 1

16x+x^2+2x=11-2x+2x \\ \\ x^2+18x=11 \\ \\ x^2+18x-11=11-11 \\ \\ x^2+18x-11=0 \\ \\ Formula : a=1,\:b=18,\:c=-11:\quad x_{1,\:2}=\frac{-18\pm \sqrt{18^2-4\cdot \:1\left(-11\right)}}{2\cdot \:1} \\ \\ \frac{-18+\sqrt{18^2-4\cdot \:1\cdot \left(-11\right)}}{2\cdot \:1} \\ \\ =\frac{-18+\sqrt{18^2-\left(-11\right)\cdot \:1\cdot \:4}}{2} \\ \\ \sqrt{18^2-4\cdot \:1\cdot \left(-11\right)}=\sqrt{18^2+1\cdot \:4\cdot \:11}=\sqrt{324+1\cdot \:4\cdot \:11} \\ \\ [/tex][tex]=\sqrt{324+44} \\ \\ =\sqrt{368} \\ \\ =\frac{-18+\sqrt{368}}{2} \\ \\ \sqrt{368}=4\sqrt{23} \\ \\ =\frac{-18+4\sqrt{23}}{2} \\ \\ -18+4\sqrt{23}=-2\cdot \:9+2\cdot \:2\sqrt{23}=2\left(2\sqrt{23}-9\right) \\ \\ =\frac{2\left(2\sqrt{23}-9\right)}{2} \\ \\ =2\sqrt{23}-9 \\ \\ x=2\sqrt{23}-9,\:x=-2\sqrt{23}-9[/tex]