Whakaoti i te 120000=112(1102)(x/1000)^2

$$120000 = 112 ( 1102 ) ( \frac { x } { 1000 } ) ^ { 2 }$$

Whakaoti mō x

$$x = \frac{25000 \sqrt{23142}}{3857} \approx 986.031557196$$

$$x = -\frac{25000 \sqrt{23142}}{3857} \approx -986.031557196$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te 112 ki te 1102, ka 123424.

$$120000=123424\times \left(\frac{x}{1000}\right)^{2}$$

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

$$120000=123424\times \frac{x^{2}}{1000^{2}}$$

Tuhia te 123424\times \frac{x^{2}}{1000^{2}} hei hautanga kotahi.

$$120000=\frac{123424x^{2}}{1000^{2}}$$

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

$$120000=\frac{123424x^{2}}{1000000}$$

Whakawehea te 123424x^{2} ki te 1000000, kia riro ko \frac{3857}{31250}x^{2}.

$$120000=\frac{3857}{31250}x^{2}$$

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

$$\frac{3857}{31250}x^{2}=120000$$

Me whakarea ngā taha e rua ki te \frac{31250}{3857}, te tau utu o \frac{3857}{31250}.

$$x^{2}=120000\times \frac{31250}{3857}$$

Whakareatia te 120000 ki te \frac{31250}{3857}, ka \frac{3750000000}{3857}.

$$x^{2}=\frac{3750000000}{3857}$$

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

$$x=\frac{25000\sqrt{23142}}{3857} x=-\frac{25000\sqrt{23142}}{3857}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 112 ki te 1102, ka 123424.

$$120000=123424\times \left(\frac{x}{1000}\right)^{2}$$

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

$$120000=123424\times \frac{x^{2}}{1000^{2}}$$

Tuhia te 123424\times \frac{x^{2}}{1000^{2}} hei hautanga kotahi.

$$120000=\frac{123424x^{2}}{1000^{2}}$$

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

$$120000=\frac{123424x^{2}}{1000000}$$

Whakawehea te 123424x^{2} ki te 1000000, kia riro ko \frac{3857}{31250}x^{2}.

$$120000=\frac{3857}{31250}x^{2}$$

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

$$\frac{3857}{31250}x^{2}=120000$$

Tangohia te 120000 mai i ngā taha e rua.

$$\frac{3857}{31250}x^{2}-120000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{3857}{31250} mō a, 0 mō b, me -120000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3857}{31250}\left(-120000\right)}}{2\times \frac{3857}{31250}}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times \frac{3857}{31250}\left(-120000\right)}}{2\times \frac{3857}{31250}}$$

Whakareatia -4 ki te \frac{3857}{31250}.

$$x=\frac{0±\sqrt{-\frac{7714}{15625}\left(-120000\right)}}{2\times \frac{3857}{31250}}$$

Whakareatia -\frac{7714}{15625} ki te -120000.

$$x=\frac{0±\sqrt{\frac{1481088}{25}}}{2\times \frac{3857}{31250}}$$

Tuhia te pūtakerua o te \frac{1481088}{25}.

$$x=\frac{0±\frac{8\sqrt{23142}}{5}}{2\times \frac{3857}{31250}}$$

Whakareatia 2 ki te \frac{3857}{31250}.

$$x=\frac{0±\frac{8\sqrt{23142}}{5}}{\frac{3857}{15625}}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{8\sqrt{23142}}{5}}{\frac{3857}{15625}} ina he tāpiri te ±.

$$x=\frac{25000\sqrt{23142}}{3857}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{8\sqrt{23142}}{5}}{\frac{3857}{15625}} ina he tango te ±.

$$x=-\frac{25000\sqrt{23142}}{3857}$$

Kua oti te whārite te whakatau.

$$x=\frac{25000\sqrt{23142}}{3857} x=-\frac{25000\sqrt{23142}}{3857}$$