Whakaoti i te 1/2*3*t^2=15t

$$\frac { 1 } { 2 } \cdot 3 \cdot t ^ { 2 } = 15 t$$

Whakaoti mō t

$$t=10$$

$$t=0$$

Ngā Upane Whakamahi Tauwehe

Whakareatia te \frac{1}{2} ki te 3, ka \frac{3}{2}.

$$\frac{3}{2}t^{2}=15t$$

Tangohia te 15t mai i ngā taha e rua.

$$\frac{3}{2}t^{2}-15t=0$$

Tauwehea te t.

$$t\left(\frac{3}{2}t-15\right)=0$$

Hei kimi otinga whārite, me whakaoti te t=0 me te \frac{3t}{2}-15=0.

$$t=0 t=10$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te \frac{1}{2} ki te 3, ka \frac{3}{2}.

$$\frac{3}{2}t^{2}=15t$$

Tangohia te 15t mai i ngā taha e rua.

$$\frac{3}{2}t^{2}-15t=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{3}{2} mō a, -15 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}}}{2\times \frac{3}{2}}$$

Tuhia te pūtakerua o te \left(-15\right)^{2}.

$$t=\frac{-\left(-15\right)±15}{2\times \frac{3}{2}}$$

Ko te tauaro o -15 ko 15.

$$t=\frac{15±15}{2\times \frac{3}{2}}$$

Whakareatia 2 ki te \frac{3}{2}.

$$t=\frac{15±15}{3}$$

Nā, me whakaoti te whārite t=\frac{15±15}{3} ina he tāpiri te ±. Tāpiri 15 ki te 15.

$$t=\frac{30}{3}$$

Whakawehe 30 ki te 3.

$$t=10$$

Nā, me whakaoti te whārite t=\frac{15±15}{3} ina he tango te ±. Tango 15 mai i 15.

$$t=\frac{0}{3}$$

Whakawehe 0 ki te 3.

$$t=0$$

Kua oti te whārite te whakatau.

$$t=10 t=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te \frac{1}{2} ki te 3, ka \frac{3}{2}.

$$\frac{3}{2}t^{2}=15t$$

Tangohia te 15t mai i ngā taha e rua.

$$\frac{3}{2}t^{2}-15t=0$$

Whakawehea ngā taha e rua o te whārite ki te \frac{3}{2}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{\frac{3}{2}t^{2}-15t}{\frac{3}{2}}=\frac{0}{\frac{3}{2}}$$

Mā te whakawehe ki te \frac{3}{2} ka wetekia te whakareanga ki te \frac{3}{2}.

$$t^{2}+\left(-\frac{15}{\frac{3}{2}}\right)t=\frac{0}{\frac{3}{2}}$$

Whakawehe -15 ki te \frac{3}{2} mā te whakarea -15 ki te tau huripoki o \frac{3}{2}.

$$t^{2}-10t=\frac{0}{\frac{3}{2}}$$

Whakawehe 0 ki te \frac{3}{2} mā te whakarea 0 ki te tau huripoki o \frac{3}{2}.

$$t^{2}-10t=0$$

Whakawehea te -10, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -5. Nā, tāpiria te pūrua o te -5 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-10t+\left(-5\right)^{2}=\left(-5\right)^{2}$$

Pūrua -5.

$$t^{2}-10t+25=25$$

Tauwehea t^{2}-10t+25. 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}.

$$\left(t-5\right)^{2}=25$$

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

$$\sqrt{\left(t-5\right)^{2}}=\sqrt{25}$$

Whakarūnātia.

$$t-5=5 t-5=-5$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$t=10 t=0$$