Whakaoti i te x^0=frac{30+4^2+sqrt{8}1+5^2x5}{4x+15+2(6-5)}

$$x ^ { 0 } = \frac { 30 + 4 ^ { 2 } + \sqrt { 8 } 1 + 5 ^ { 2 } x 5 } { 4 x + 15 + 2 ( 6 - 5 ) }$$

Whakaoti mō x_5

$$x_{5}=\frac{4x-2\sqrt{2}-29}{25}$$

$$x\neq 0\text{ and }x\neq -\frac{17}{4}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 4x+17.

$$\left(4x+17\right)x^{0}=30+4^{2}+1\sqrt{8}+5^{2}x_{5}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x+17 ki te x^{0}.

$$4xx^{0}+17x^{0}=30+4^{2}+1\sqrt{8}+5^{2}x_{5}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 0 kia riro ai te 1.

$$4x^{1}+17x^{0}=30+4^{2}+1\sqrt{8}+5^{2}x_{5}$$

Tātaihia te x mā te pū o 1, kia riro ko x.

$$4x+17x^{0}=30+4^{2}+1\sqrt{8}+5^{2}x_{5}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$4x+17x^{0}=30+16+1\sqrt{8}+5^{2}x_{5}$$

Tāpirihia te 30 ki te 16, ka 46.

$$4x+17x^{0}=46+1\sqrt{8}+5^{2}x_{5}$$

Tauwehea te 8=2^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 2} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{2}. Tuhia te pūtakerua o te 2^{2}.

$$4x+17x^{0}=46+1\times 2\sqrt{2}+5^{2}x_{5}$$

Whakareatia te 1 ki te 2, ka 2.

$$4x+17x^{0}=46+2\sqrt{2}+5^{2}x_{5}$$

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$4x+17x^{0}=46+2\sqrt{2}+25x_{5}$$

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

$$46+2\sqrt{2}+25x_{5}=4x+17x^{0}$$

Tangohia te 46 mai i ngā taha e rua.

$$2\sqrt{2}+25x_{5}=4x+17x^{0}-46$$

Tangohia te 2\sqrt{2} mai i ngā taha e rua.

$$25x_{5}=4x+17x^{0}-46-2\sqrt{2}$$

He hanga arowhānui tō te whārite.

$$25x_{5}=4x-2\sqrt{2}-29$$

Whakawehea ngā taha e rua ki te 25.

$$\frac{25x_{5}}{25}=\frac{4x-2\sqrt{2}-29}{25}$$

Mā te whakawehe ki te 25 ka wetekia te whakareanga ki te 25.

$$x_{5}=\frac{4x-2\sqrt{2}-29}{25}$$

Whakaoti mō x (complex solution)

$$x=\frac{25x_{5}}{4}+\frac{\sqrt{2}}{2}+\frac{29}{4}$$

$$x_{5}\neq \frac{-2\sqrt{2}-29}{25}\text{ and }x_{5}\neq \frac{-2\sqrt{2}-46}{25}\text{ and }x_{5}\neq \frac{-2\sqrt{2}-29}{25}$$

Whakaoti mō x

$$x=\frac{25x_{5}}{4}+\frac{\sqrt{2}}{2}+\frac{29}{4}$$

$$x_{5}\neq \frac{-2\sqrt{2}-29}{25}\text{ and }x_{5}\neq \frac{-2\sqrt{2}-46}{25}$$