Whakaoti i te 0=x^2-100x+560000

$$0 = x ^ { 2 } - 100 x + 560000$$

Whakaoti mō x (complex solution)

$$x=50+50\sqrt{223}i\approx 50+746.659226153i$$

$$x=-50\sqrt{223}i+50\approx 50-746.659226153i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$x^{2}-100x+560000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -100 mō b, me 560000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-100\right)±\sqrt{\left(-100\right)^{2}-4\times 560000}}{2}$$

Pūrua -100.

$$x=\frac{-\left(-100\right)±\sqrt{10000-4\times 560000}}{2}$$

Whakareatia -4 ki te 560000.

$$x=\frac{-\left(-100\right)±\sqrt{10000-2240000}}{2}$$

Tāpiri 10000 ki te -2240000.

$$x=\frac{-\left(-100\right)±\sqrt{-2230000}}{2}$$

Tuhia te pūtakerua o te -2230000.

$$x=\frac{-\left(-100\right)±100\sqrt{223}i}{2}$$

Ko te tauaro o -100 ko 100.

$$x=\frac{100±100\sqrt{223}i}{2}$$

Nā, me whakaoti te whārite x=\frac{100±100\sqrt{223}i}{2} ina he tāpiri te ±. Tāpiri 100 ki te 100i\sqrt{223}.

$$x=\frac{100+100\sqrt{223}i}{2}$$

Whakawehe 100+100i\sqrt{223} ki te 2.

$$x=50+50\sqrt{223}i$$

Nā, me whakaoti te whārite x=\frac{100±100\sqrt{223}i}{2} ina he tango te ±. Tango 100i\sqrt{223} mai i 100.

$$x=\frac{-100\sqrt{223}i+100}{2}$$

Whakawehe 100-100i\sqrt{223} ki te 2.

$$x=-50\sqrt{223}i+50$$

Kua oti te whārite te whakatau.

$$x=50+50\sqrt{223}i x=-50\sqrt{223}i+50$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$x^{2}-100x+560000=0$$

Tangohia te 560000 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-100x=-560000$$

Whakawehea te -100, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -50. Nā, tāpiria te pūrua o te -50 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-100x+\left(-50\right)^{2}=-560000+\left(-50\right)^{2}$$

Pūrua -50.

$$x^{2}-100x+2500=-560000+2500$$

Tāpiri -560000 ki te 2500.

$$x^{2}-100x+2500=-557500$$

Tauwehea x^{2}-100x+2500. 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}.

$$\left(x-50\right)^{2}=-557500$$

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

$$\sqrt{\left(x-50\right)^{2}}=\sqrt{-557500}$$

Whakarūnātia.

$$x-50=50\sqrt{223}i x-50=-50\sqrt{223}i$$

Me tāpiri 50 ki ngā taha e rua o te whārite.

$$x=50+50\sqrt{223}i x=-50\sqrt{223}i+50$$