Whakaoti i te 120000=1.12*81.2{left(x/1000right)}^2

$$120000 = 1.12 \cdot 81.2 { \left( \frac{ x }{ 1000 } \right) }^{ 2 }$$

Whakaoti mō x

$$x = \frac{250000 \sqrt{870}}{203} \approx 36324.830551115$$

$$x = -\frac{250000 \sqrt{870}}{203} \approx -36324.830551115$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te 1.12 ki te 81.2, ka 90.944.

$$120000=90.944\times \left(\frac{x}{1000}\right)^{2}$$

Kia whakarewa i te \frac{x}{1000} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$120000=90.944\times \frac{x^{2}}{1000^{2}}$$

Tātaihia te 1000 mā te pū o 2, kia riro ko 1000000.

$$120000=90.944\times \frac{x^{2}}{1000000}$$

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

$$90.944\times \frac{x^{2}}{1000000}=120000$$

Whakawehea ngā taha e rua ki te 90.944.

$$\frac{x^{2}}{1000000}=\frac{120000}{90.944}$$

Whakarohaina te \frac{120000}{90.944} mā te whakarea i te taurunga me te tauraro ki te 1000.

$$\frac{x^{2}}{1000000}=\frac{120000000}{90944}$$

Whakahekea te hautanga \frac{120000000}{90944} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 64.

$$\frac{x^{2}}{1000000}=\frac{1875000}{1421}$$

Me whakarea ngā taha e rua ki te 1000000.

$$x^{2}=\frac{1875000}{1421}\times 1000000$$

Whakareatia te \frac{1875000}{1421} ki te 1000000, ka \frac{1875000000000}{1421}.

$$x^{2}=\frac{1875000000000}{1421}$$

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

$$x=\frac{250000\sqrt{870}}{203} x=-\frac{250000\sqrt{870}}{203}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 1.12 ki te 81.2, ka 90.944.

$$120000=90.944\times \left(\frac{x}{1000}\right)^{2}$$

Kia whakarewa i te \frac{x}{1000} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$120000=90.944\times \frac{x^{2}}{1000^{2}}$$

Tātaihia te 1000 mā te pū o 2, kia riro ko 1000000.

$$120000=90.944\times \frac{x^{2}}{1000000}$$

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

$$90.944\times \frac{x^{2}}{1000000}=120000$$

Tangohia te 120000 mai i ngā taha e rua.

$$90.944\times \frac{x^{2}}{1000000}-120000=0$$

Whakareatia ngā taha e rua o te whārite ki te 1000000.

$$90.944x^{2}-120000000000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 90.944 mō a, 0 mō b, me -120000000000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 90.944\left(-120000000000\right)}}{2\times 90.944}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 90.944\left(-120000000000\right)}}{2\times 90.944}$$

Whakareatia -4 ki te 90.944.

$$x=\frac{0±\sqrt{-363.776\left(-120000000000\right)}}{2\times 90.944}$$

Whakareatia -363.776 ki te -120000000000.

$$x=\frac{0±\sqrt{43653120000000}}{2\times 90.944}$$

Tuhia te pūtakerua o te 43653120000000.

$$x=\frac{0±224000\sqrt{870}}{2\times 90.944}$$

Whakareatia 2 ki te 90.944.

$$x=\frac{0±224000\sqrt{870}}{181.888}$$

Nā, me whakaoti te whārite x=\frac{0±224000\sqrt{870}}{181.888} ina he tāpiri te ±.

$$x=\frac{250000\sqrt{870}}{203}$$

Nā, me whakaoti te whārite x=\frac{0±224000\sqrt{870}}{181.888} ina he tango te ±.

$$x=-\frac{250000\sqrt{870}}{203}$$

Kua oti te whārite te whakatau.

$$x=\frac{250000\sqrt{870}}{203} x=-\frac{250000\sqrt{870}}{203}$$