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

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

Whakaoti mō x_2

$$x_{2}=-\frac{-x^{2}-17x-34\sqrt{x}+112.04368456589644616}{\sqrt{x}\left(x+2\sqrt{x}-6.06139320975861448\right)}$$

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Evaluate trigonometric functions in the problem

$$x ^ {2} = 9 + {(17 - x 2 \sqrt{x})} \cdot {({(7 - x - 2 \sqrt{x})} - 6 \cdot 0.15643446504023092)}$$

Whakareatia te 6 ki te 0.15643446504023092, ka 0.93860679024138552.

$$x^{2}=9+\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}-0.93860679024138552\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 17-x_{2}\sqrt{x} ki te 7-x-2\sqrt{x}-0.93860679024138552.

$$x^{2}=9+\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}\right)-0.93860679024138552\left(17-x_{2}\sqrt{x}\right)$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$9+\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}\right)-0.93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}$$

Tangohia te 9 mai i ngā taha e rua.

$$\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}\right)-0.93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}-9$$

Whakamahia te āhuatanga tohatoha hei whakarea te 17-x_{2}\sqrt{x} ki te 7-x-2\sqrt{x}.

$$119-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}\left(\sqrt{x}\right)^{2}-0.93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}-9$$

Tātaihia te \sqrt{x} mā te pū o 2, kia riro ko x.

$$119-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x-0.93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}-9$$

Whakamahia te āhuatanga tohatoha hei whakarea te -0.93860679024138552 ki te 17-x_{2}\sqrt{x}.

$$119-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x-15.95631543410355384+0.93860679024138552x_{2}\sqrt{x}=x^{2}-9$$

Tangohia te 15.95631543410355384 i te 119, ka 103.04368456589644616.

$$103.04368456589644616-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x+0.93860679024138552x_{2}\sqrt{x}=x^{2}-9$$

Pahekotia te -7x_{2}\sqrt{x} me 0.93860679024138552x_{2}\sqrt{x}, ka -6.06139320975861448x_{2}\sqrt{x}.

$$103.04368456589644616-17x-34\sqrt{x}-6.06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-9$$

Tangohia te 103.04368456589644616 mai i ngā taha e rua.

$$-17x-34\sqrt{x}-6.06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-9-103.04368456589644616$$

Tangohia te 103.04368456589644616 i te -9, ka -112.04368456589644616.

$$-17x-34\sqrt{x}-6.06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-112.04368456589644616$$

Me tāpiri te 17x ki ngā taha e rua.

$$-34\sqrt{x}-6.06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-112.04368456589644616+17x$$

Me tāpiri te 34\sqrt{x} ki ngā taha e rua.

$$-6.06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-112.04368456589644616+17x+34\sqrt{x}$$

Pahekotia ngā kīanga tau katoa e whai ana i te x_{2}.

$$\left(-6.06139320975861448\sqrt{x}+x\sqrt{x}+2x\right)x_{2}=x^{2}-112.04368456589644616+17x+34\sqrt{x}$$

He hanga arowhānui tō te whārite.

$$\left(\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}\right)x_{2}=x^{2}+17x+34\sqrt{x}-112.04368456589644616$$

Whakawehea ngā taha e rua ki te -6.06139320975861448\sqrt{x}+x\sqrt{x}+2x.

$$\frac{\left(\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}\right)x_{2}}{\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}}=\frac{x^{2}+17x+34\sqrt{x}-112.04368456589644616}{\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}}$$

Mā te whakawehe ki te -6.06139320975861448\sqrt{x}+x\sqrt{x}+2x ka wetekia te whakareanga ki te -6.06139320975861448\sqrt{x}+x\sqrt{x}+2x.

$$x_{2}=\frac{x^{2}+17x+34\sqrt{x}-112.04368456589644616}{\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}}$$

Whakawehe x^{2}-112.04368456589644616+17x+34\sqrt{x} ki te -6.06139320975861448\sqrt{x}+x\sqrt{x}+2x.

$$x_{2}=\frac{x^{2}+17x+34\sqrt{x}-112.04368456589644616}{\sqrt{x}\left(x+2\sqrt{x}-6.06139320975861448\right)}$$