Whakaoti i te x^2-105x+244=0

$$x ^ { 2 } - 105 x + 244 = 0$$

Whakaoti mō x

$$x = \frac{\sqrt{10049} + 105}{2} \approx 102.622350304$$

$$x = \frac{105 - \sqrt{10049}}{2} \approx 2.377649696$$

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.

$$x^{2}-105x+244=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -105 mō b, me 244 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-105\right)±\sqrt{\left(-105\right)^{2}-4\times 244}}{2}$$

Pūrua -105.

$$x=\frac{-\left(-105\right)±\sqrt{11025-4\times 244}}{2}$$

Whakareatia -4 ki te 244.

$$x=\frac{-\left(-105\right)±\sqrt{11025-976}}{2}$$

Tāpiri 11025 ki te -976.

$$x=\frac{-\left(-105\right)±\sqrt{10049}}{2}$$

Ko te tauaro o -105 ko 105.

$$x=\frac{105±\sqrt{10049}}{2}$$

Nā, me whakaoti te whārite x=\frac{105±\sqrt{10049}}{2} ina he tāpiri te ±. Tāpiri 105 ki te \sqrt{10049}.

$$x=\frac{\sqrt{10049}+105}{2}$$

Nā, me whakaoti te whārite x=\frac{105±\sqrt{10049}}{2} ina he tango te ±. Tango \sqrt{10049} mai i 105.

$$x=\frac{105-\sqrt{10049}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{10049}+105}{2} x=\frac{105-\sqrt{10049}}{2}$$

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.

$$x^{2}-105x+244=0$$

Me tango 244 mai i ngā taha e rua o te whārite.

$$x^{2}-105x+244-244=-244$$

Mā te tango i te 244 i a ia ake anō ka toe ko te 0.

$$x^{2}-105x=-244$$

Whakawehea te -105, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{105}{2}. Nā, tāpiria te pūrua o te -\frac{105}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-105x+\left(-\frac{105}{2}\right)^{2}=-244+\left(-\frac{105}{2}\right)^{2}$$

Pūruatia -\frac{105}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-105x+\frac{11025}{4}=-244+\frac{11025}{4}$$

Tāpiri -244 ki te \frac{11025}{4}.

$$x^{2}-105x+\frac{11025}{4}=\frac{10049}{4}$$

Tauwehea x^{2}-105x+\frac{11025}{4}. 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}.

$$\left(x-\frac{105}{2}\right)^{2}=\frac{10049}{4}$$

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

$$\sqrt{\left(x-\frac{105}{2}\right)^{2}}=\sqrt{\frac{10049}{4}}$$

Whakarūnātia.

$$x-\frac{105}{2}=\frac{\sqrt{10049}}{2} x-\frac{105}{2}=-\frac{\sqrt{10049}}{2}$$

Me tāpiri \frac{105}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{10049}+105}{2} x=\frac{105-\sqrt{10049}}{2}$$