Whakaoti i te 4.4t^2-2.44t=0

$$4.4 t ^ { 2 } - 2.44 t = 0$$

Whakaoti mō t

$$t=\frac{61}{110}\approx 0.554545455$$

$$t=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te t.

$$t\left(4.4t-2.44\right)=0$$

Hei kimi otinga whārite, me whakaoti te t=0 me te \frac{22t}{5}-2.44=0.

$$t=0 t=\frac{61}{110}$$

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.

$$4.4t^{2}-2.44t=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4.4 mō a, -2.44 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-2.44\right)±\sqrt{\left(-2.44\right)^{2}}}{2\times 4.4}$$

Tuhia te pūtakerua o te \left(-2.44\right)^{2}.

$$t=\frac{-\left(-2.44\right)±\frac{61}{25}}{2\times 4.4}$$

Ko te tauaro o -2.44 ko 2.44.

$$t=\frac{2.44±\frac{61}{25}}{2\times 4.4}$$

Whakareatia 2 ki te 4.4.

$$t=\frac{2.44±\frac{61}{25}}{8.8}$$

Nā, me whakaoti te whārite t=\frac{2.44±\frac{61}{25}}{8.8} ina he tāpiri te ±. Tāpiri 2.44 ki te \frac{61}{25} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$t=\frac{\frac{122}{25}}{8.8}$$

Whakawehe \frac{122}{25} ki te 8.8 mā te whakarea \frac{122}{25} ki te tau huripoki o 8.8.

$$t=\frac{61}{110}$$

Nā, me whakaoti te whārite t=\frac{2.44±\frac{61}{25}}{8.8} ina he tango te ±. Tango \frac{61}{25} mai i 2.44 mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$t=\frac{0}{8.8}$$

Whakawehe 0 ki te 8.8 mā te whakarea 0 ki te tau huripoki o 8.8.

$$t=0$$

Kua oti te whārite te whakatau.

$$t=\frac{61}{110} t=0$$

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.

$$4.4t^{2}-2.44t=0$$

Whakawehea ngā taha e rua o te whārite ki te 4.4, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{4.4t^{2}-2.44t}{4.4}=\frac{0}{4.4}$$

Mā te whakawehe ki te 4.4 ka wetekia te whakareanga ki te 4.4.

$$t^{2}+\left(-\frac{2.44}{4.4}\right)t=\frac{0}{4.4}$$

Whakawehe -2.44 ki te 4.4 mā te whakarea -2.44 ki te tau huripoki o 4.4.

$$t^{2}-\frac{61}{110}t=\frac{0}{4.4}$$

Whakawehe 0 ki te 4.4 mā te whakarea 0 ki te tau huripoki o 4.4.

$$t^{2}-\frac{61}{110}t=0$$

Whakawehea te -\frac{61}{110}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{61}{220}. Nā, tāpiria te pūrua o te -\frac{61}{220} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-\frac{61}{110}t+\left(-\frac{61}{220}\right)^{2}=\left(-\frac{61}{220}\right)^{2}$$

Pūruatia -\frac{61}{220} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-\frac{61}{110}t+\frac{3721}{48400}=\frac{3721}{48400}$$

Tauwehea t^{2}-\frac{61}{110}t+\frac{3721}{48400}. 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}.

$$\left(t-\frac{61}{220}\right)^{2}=\frac{3721}{48400}$$

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

$$\sqrt{\left(t-\frac{61}{220}\right)^{2}}=\sqrt{\frac{3721}{48400}}$$

Whakarūnātia.

$$t-\frac{61}{220}=\frac{61}{220} t-\frac{61}{220}=-\frac{61}{220}$$

Me tāpiri \frac{61}{220} ki ngā taha e rua o te whārite.

$$t=\frac{61}{110} t=0$$