Whakaoti i te t^2-13t-8=0

$$t ^ { 2 } - 13 t - 8 = 0$$

Whakaoti mō t

$$t = \frac{\sqrt{201} + 13}{2} \approx 13.588723439$$

$$t=\frac{13-\sqrt{201}}{2}\approx -0.588723439$$

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.

$$t^{2}-13t-8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -13 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\left(-8\right)}}{2}$$

Pūrua -13.

$$t=\frac{-\left(-13\right)±\sqrt{169-4\left(-8\right)}}{2}$$

Whakareatia -4 ki te -8.

$$t=\frac{-\left(-13\right)±\sqrt{169+32}}{2}$$

Tāpiri 169 ki te 32.

$$t=\frac{-\left(-13\right)±\sqrt{201}}{2}$$

Ko te tauaro o -13 ko 13.

$$t=\frac{13±\sqrt{201}}{2}$$

Nā, me whakaoti te whārite t=\frac{13±\sqrt{201}}{2} ina he tāpiri te ±. Tāpiri 13 ki te \sqrt{201}.

$$t=\frac{\sqrt{201}+13}{2}$$

Nā, me whakaoti te whārite t=\frac{13±\sqrt{201}}{2} ina he tango te ±. Tango \sqrt{201} mai i 13.

$$t=\frac{13-\sqrt{201}}{2}$$

Kua oti te whārite te whakatau.

$$t=\frac{\sqrt{201}+13}{2} t=\frac{13-\sqrt{201}}{2}$$

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.

$$t^{2}-13t-8=0$$

Me tāpiri 8 ki ngā taha e rua o te whārite.

$$t^{2}-13t-8-\left(-8\right)=-\left(-8\right)$$

Mā te tango i te -8 i a ia ake anō ka toe ko te 0.

$$t^{2}-13t=-\left(-8\right)$$

Tango -8 mai i 0.

$$t^{2}-13t=8$$

Whakawehea te -13, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{13}{2}. Nā, tāpiria te pūrua o te -\frac{13}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-13t+\left(-\frac{13}{2}\right)^{2}=8+\left(-\frac{13}{2}\right)^{2}$$

Pūruatia -\frac{13}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-13t+\frac{169}{4}=8+\frac{169}{4}$$

Tāpiri 8 ki te \frac{169}{4}.

$$t^{2}-13t+\frac{169}{4}=\frac{201}{4}$$

Tauwehea t^{2}-13t+\frac{169}{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}.

$$\left(t-\frac{13}{2}\right)^{2}=\frac{201}{4}$$

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

$$\sqrt{\left(t-\frac{13}{2}\right)^{2}}=\sqrt{\frac{201}{4}}$$

Whakarūnātia.

$$t-\frac{13}{2}=\frac{\sqrt{201}}{2} t-\frac{13}{2}=-\frac{\sqrt{201}}{2}$$

Me tāpiri \frac{13}{2} ki ngā taha e rua o te whārite.

$$t=\frac{\sqrt{201}+13}{2} t=\frac{13-\sqrt{201}}{2}$$