Whakaoti i te x^2-180x+2000=0

$$x ^ { 2 } - 180 x + 2000 = 0$$

Whakaoti mō x

$$x=10\sqrt{61}+90\approx 168.102496759$$

$$x=90-10\sqrt{61}\approx 11.897503241$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x^{2}-180x+2000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -180 mō b, me 2000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-180\right)±\sqrt{\left(-180\right)^{2}-4\times 2000}}{2}$$

Pūrua -180.

$$x=\frac{-\left(-180\right)±\sqrt{32400-4\times 2000}}{2}$$

Whakareatia -4 ki te 2000.

$$x=\frac{-\left(-180\right)±\sqrt{32400-8000}}{2}$$

Tāpiri 32400 ki te -8000.

$$x=\frac{-\left(-180\right)±\sqrt{24400}}{2}$$

Tuhia te pūtakerua o te 24400.

$$x=\frac{-\left(-180\right)±20\sqrt{61}}{2}$$

Ko te tauaro o -180 ko 180.

$$x=\frac{180±20\sqrt{61}}{2}$$

Nā, me whakaoti te whārite x=\frac{180±20\sqrt{61}}{2} ina he tāpiri te ±. Tāpiri 180 ki te 20\sqrt{61}.

$$x=\frac{20\sqrt{61}+180}{2}$$

Whakawehe 180+20\sqrt{61} ki te 2.

$$x=10\sqrt{61}+90$$

Nā, me whakaoti te whārite x=\frac{180±20\sqrt{61}}{2} ina he tango te ±. Tango 20\sqrt{61} mai i 180.

$$x=\frac{180-20\sqrt{61}}{2}$$

Whakawehe 180-20\sqrt{61} ki te 2.

$$x=90-10\sqrt{61}$$

Kua oti te whārite te whakatau.

$$x=10\sqrt{61}+90 x=90-10\sqrt{61}$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$x^{2}-180x+2000=0$$

Me tango 2000 mai i ngā taha e rua o te whārite.

$$x^{2}-180x+2000-2000=-2000$$

Mā te tango i te 2000 i a ia ake anō ka toe ko te 0.

$$x^{2}-180x=-2000$$

Whakawehea te -180, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -90. Nā, tāpiria te pūrua o te -90 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-180x+\left(-90\right)^{2}=-2000+\left(-90\right)^{2}$$

Pūrua -90.

$$x^{2}-180x+8100=-2000+8100$$

Tāpiri -2000 ki te 8100.

$$x^{2}-180x+8100=6100$$

Tauwehea x^{2}-180x+8100. 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}.

$$\left(x-90\right)^{2}=6100$$

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

$$\sqrt{\left(x-90\right)^{2}}=\sqrt{6100}$$

Whakarūnātia.

$$x-90=10\sqrt{61} x-90=-10\sqrt{61}$$

Me tāpiri 90 ki ngā taha e rua o te whārite.

$$x=10\sqrt{61}+90 x=90-10\sqrt{61}$$