Whakaoti i te x^2-406x+163^2=0

$${ x }^{ 2 } -406x+ { 163 }^{ 2 } =0$$

Whakaoti mō x

$$x=4\sqrt{915}+203\approx 323.995867698$$

$$x=203-4\sqrt{915}\approx 82.004132302$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 163 mā te pū o 2, kia riro ko 26569.

$$x^{2}-406x+26569=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -406 mō b, me 26569 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-406\right)±\sqrt{\left(-406\right)^{2}-4\times 26569}}{2}$$

Pūrua -406.

$$x=\frac{-\left(-406\right)±\sqrt{164836-4\times 26569}}{2}$$

Whakareatia -4 ki te 26569.

$$x=\frac{-\left(-406\right)±\sqrt{164836-106276}}{2}$$

Tāpiri 164836 ki te -106276.

$$x=\frac{-\left(-406\right)±\sqrt{58560}}{2}$$

Tuhia te pūtakerua o te 58560.

$$x=\frac{-\left(-406\right)±8\sqrt{915}}{2}$$

Ko te tauaro o -406 ko 406.

$$x=\frac{406±8\sqrt{915}}{2}$$

Nā, me whakaoti te whārite x=\frac{406±8\sqrt{915}}{2} ina he tāpiri te ±. Tāpiri 406 ki te 8\sqrt{915}.

$$x=\frac{8\sqrt{915}+406}{2}$$

Whakawehe 406+8\sqrt{915} ki te 2.

$$x=4\sqrt{915}+203$$

Nā, me whakaoti te whārite x=\frac{406±8\sqrt{915}}{2} ina he tango te ±. Tango 8\sqrt{915} mai i 406.

$$x=\frac{406-8\sqrt{915}}{2}$$

Whakawehe 406-8\sqrt{915} ki te 2.

$$x=203-4\sqrt{915}$$

Kua oti te whārite te whakatau.

$$x=4\sqrt{915}+203 x=203-4\sqrt{915}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tātaihia te 163 mā te pū o 2, kia riro ko 26569.

$$x^{2}-406x+26569=0$$

Tangohia te 26569 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-406x=-26569$$

Whakawehea te -406, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -203. Nā, tāpiria te pūrua o te -203 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-406x+\left(-203\right)^{2}=-26569+\left(-203\right)^{2}$$

Pūrua -203.

$$x^{2}-406x+41209=-26569+41209$$

Tāpiri -26569 ki te 41209.

$$x^{2}-406x+41209=14640$$

Tauwehea x^{2}-406x+41209. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-203\right)^{2}=14640$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x-203\right)^{2}}=\sqrt{14640}$$

Whakarūnātia.

$$x-203=4\sqrt{915} x-203=-4\sqrt{915}$$

Me tāpiri 203 ki ngā taha e rua o te whārite.

$$x=4\sqrt{915}+203 x=203-4\sqrt{915}$$