Whakaoti i te t^2+6t-7.2=0

$$t ^ { 2 } + 6 t - 7.2 = 0$$

Whakaoti mō t

$$t=\frac{9\sqrt{5}}{5}-3\approx 1.024922359$$

$$t=-\frac{9\sqrt{5}}{5}-3\approx -7.024922359$$

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.

$$t^{2}+6t-7.2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 6 mō b, me -7.2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-6±\sqrt{6^{2}-4\left(-7.2\right)}}{2}$$

Pūrua 6.

$$t=\frac{-6±\sqrt{36-4\left(-7.2\right)}}{2}$$

Whakareatia -4 ki te -7.2.

$$t=\frac{-6±\sqrt{36+28.8}}{2}$$

Tāpiri 36 ki te 28.8.

$$t=\frac{-6±\sqrt{64.8}}{2}$$

Tuhia te pūtakerua o te 64.8.

$$t=\frac{-6±\frac{18\sqrt{5}}{5}}{2}$$

Nā, me whakaoti te whārite t=\frac{-6±\frac{18\sqrt{5}}{5}}{2} ina he tāpiri te ±. Tāpiri -6 ki te \frac{18\sqrt{5}}{5}.

$$t=\frac{\frac{18\sqrt{5}}{5}-6}{2}$$

Whakawehe -6+\frac{18\sqrt{5}}{5} ki te 2.

$$t=\frac{9\sqrt{5}}{5}-3$$

Nā, me whakaoti te whārite t=\frac{-6±\frac{18\sqrt{5}}{5}}{2} ina he tango te ±. Tango \frac{18\sqrt{5}}{5} mai i -6.

$$t=\frac{-\frac{18\sqrt{5}}{5}-6}{2}$$

Whakawehe -6-\frac{18\sqrt{5}}{5} ki te 2.

$$t=-\frac{9\sqrt{5}}{5}-3$$

Kua oti te whārite te whakatau.

$$t=\frac{9\sqrt{5}}{5}-3 t=-\frac{9\sqrt{5}}{5}-3$$

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.

$$t^{2}+6t-7.2=0$$

Me tāpiri 7.2 ki ngā taha e rua o te whārite.

$$t^{2}+6t-7.2-\left(-7.2\right)=-\left(-7.2\right)$$

Mā te tango i te -7.2 i a ia ake anō ka toe ko te 0.

$$t^{2}+6t=-\left(-7.2\right)$$

Tango -7.2 mai i 0.

$$t^{2}+6t=7.2$$

Whakawehea te 6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 3. Nā, tāpiria te pūrua o te 3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}+6t+3^{2}=7.2+3^{2}$$

Pūrua 3.

$$t^{2}+6t+9=7.2+9$$

Tāpiri 7.2 ki te 9.

$$t^{2}+6t+9=16.2$$

Tauwehea t^{2}+6t+9. 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}.

$$\left(t+3\right)^{2}=16.2$$

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

$$\sqrt{\left(t+3\right)^{2}}=\sqrt{16.2}$$

Whakarūnātia.

$$t+3=\frac{9\sqrt{5}}{5} t+3=-\frac{9\sqrt{5}}{5}$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$t=\frac{9\sqrt{5}}{5}-3 t=-\frac{9\sqrt{5}}{5}-3$$