Rešite x^2=9+(17-x2sqrt{x})*((7-x-2sqrt{x})-6*cos81^circ)

$$x ^ { 2 } = 9 + ( 17 - x 2 \sqrt { x } ) \times ( ( 7 - x - 2 \sqrt { x } ) - 6 \cdot \cos 81 ^ { \circ } )$$

Rešitev za x_2

$$x_{2}=-\frac{-x^{2}-17x-34\sqrt{x}+112,04368456589644616}{\sqrt{x}\left(x+2\sqrt{x}-6,06139320975861448\right)}$$

$$x\neq -\frac{\sqrt{441337075609913405}}{125000000}+\frac{100767415121982681}{12500000000000000}\text{ and }x>0$$

Koraki za reševanje linearnih enačb

Evaluate trigonometric functions in the problem

$$x ^ {2} = 9 + {(17 - x 2 \sqrt{x})} \cdot {({(7 - x - 2 \sqrt{x})} - 6 \cdot 0,15643446504023092)}$$

Pomnožite 6 in 0,15643446504023092, da dobite 0,93860679024138552.

$$x^{2}=9+\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}-0,93860679024138552\right)$$

Uporabite distributivnost, da pomnožite 17-x_{2}\sqrt{x} s/z 7-x-2\sqrt{x}-0,93860679024138552.

$$x^{2}=9+\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}\right)-0,93860679024138552\left(17-x_{2}\sqrt{x}\right)$$

Zamenjajte strani tako, da so vse spremenljivke na levi strani.

$$9+\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}\right)-0,93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}$$

Odštejte 9 na obeh straneh.

$$\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}\right)-0,93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}-9$$

Uporabite distributivnost, da pomnožite 17-x_{2}\sqrt{x} s/z 7-x-2\sqrt{x}.

$$119-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}\left(\sqrt{x}\right)^{2}-0,93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}-9$$

Izračunajte potenco \sqrt{x} števila 2, da dobite x.

$$119-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x-0,93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}-9$$

Uporabite distributivnost, da pomnožite -0,93860679024138552 s/z 17-x_{2}\sqrt{x}.

$$119-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x-15,95631543410355384+0,93860679024138552x_{2}\sqrt{x}=x^{2}-9$$

Odštejte 15,95631543410355384 od 119, da dobite 103,04368456589644616.

$$103,04368456589644616-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x+0,93860679024138552x_{2}\sqrt{x}=x^{2}-9$$

Združite -7x_{2}\sqrt{x} in 0,93860679024138552x_{2}\sqrt{x}, da dobite -6,06139320975861448x_{2}\sqrt{x}.

$$103,04368456589644616-17x-34\sqrt{x}-6,06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-9$$

Odštejte 103,04368456589644616 na obeh straneh.

$$-17x-34\sqrt{x}-6,06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-9-103,04368456589644616$$

Odštejte 103,04368456589644616 od -9, da dobite -112,04368456589644616.

$$-17x-34\sqrt{x}-6,06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-112,04368456589644616$$

Dodajte 17x na obe strani.

$$-34\sqrt{x}-6,06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-112,04368456589644616+17x$$

Dodajte 34\sqrt{x} na obe strani.

$$-6,06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-112,04368456589644616+17x+34\sqrt{x}$$

Združite vse člene, ki vsebujejo x_{2}.

$$\left(-6,06139320975861448\sqrt{x}+x\sqrt{x}+2x\right)x_{2}=x^{2}-112,04368456589644616+17x+34\sqrt{x}$$

Enačba je v standardni obliki.

$$\left(\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}\right)x_{2}=x^{2}+17x+34\sqrt{x}-112,04368456589644616$$

Delite obe strani z vrednostjo -6,06139320975861448\sqrt{x}+x\sqrt{x}+2x.

$$\frac{\left(\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}\right)x_{2}}{\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}}=\frac{x^{2}+17x+34\sqrt{x}-112,04368456589644616}{\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}}$$

Z deljenjem s/z -6,06139320975861448\sqrt{x}+x\sqrt{x}+2x razveljavite množenje s/z -6,06139320975861448\sqrt{x}+x\sqrt{x}+2x.

$$x_{2}=\frac{x^{2}+17x+34\sqrt{x}-112,04368456589644616}{\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}}$$

Delite x^{2}-112,04368456589644616+17x+34\sqrt{x} s/z -6,06139320975861448\sqrt{x}+x\sqrt{x}+2x.

$$x_{2}=\frac{x^{2}+17x+34\sqrt{x}-112,04368456589644616}{\sqrt{x}\left(x+2\sqrt{x}-6,06139320975861448\right)}$$