Whakaoti i te -35t-1/2*98t^2=-14

$$- 35 t - \frac { 1 } { 2 } \times 98 t ^ { 2 } = - 14$$

Whakaoti mō t

$$t=-1$$

$$t=\frac{2}{7}\approx 0.285714286$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakareatia te \frac{1}{2} ki te 98, ka 49.

$$-35t-49t^{2}=-14$$

Me tāpiri te 14 ki ngā taha e rua.

$$-35t-49t^{2}+14=0$$

Whakawehea ngā taha e rua ki te 7.

$$-5t-7t^{2}+2=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-7t^{2}-5t+2=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -7t^{2}+at+bt+2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-5 ab=-7\times 2=-14$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -14.

$$1,-14 2,-7$$

Tātaihia te tapeke mō ia takirua.

$$1-14=-13 2-7=-5$$

Ko te otinga te takirua ka hoatu i te tapeke -5.

$$a=2 b=-7$$

Tuhia anō te -7t^{2}-5t+2 hei \left(-7t^{2}+2t\right)+\left(-7t+2\right).

$$\left(-7t^{2}+2t\right)+\left(-7t+2\right)$$

Tauwehea te -t i te tuatahi me te -1 i te rōpū tuarua.

$$-t\left(7t-2\right)-\left(7t-2\right)$$

Whakatauwehea atu te kīanga pātahi 7t-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(7t-2\right)\left(-t-1\right)$$

Hei kimi otinga whārite, me whakaoti te 7t-2=0 me te -t-1=0.

$$t=\frac{2}{7} t=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te \frac{1}{2} ki te 98, ka 49.

$$-35t-49t^{2}=-14$$

Me tāpiri te 14 ki ngā taha e rua.

$$-35t-49t^{2}+14=0$$

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.

$$-49t^{2}-35t+14=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -49 mō a, -35 mō b, me 14 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-\left(-35\right)±\sqrt{\left(-35\right)^{2}-4\left(-49\right)\times 14}}{2\left(-49\right)}$$

Pūrua -35.

$$t=\frac{-\left(-35\right)±\sqrt{1225-4\left(-49\right)\times 14}}{2\left(-49\right)}$$

Whakareatia -4 ki te -49.

$$t=\frac{-\left(-35\right)±\sqrt{1225+196\times 14}}{2\left(-49\right)}$$

Whakareatia 196 ki te 14.

$$t=\frac{-\left(-35\right)±\sqrt{1225+2744}}{2\left(-49\right)}$$

Tāpiri 1225 ki te 2744.

$$t=\frac{-\left(-35\right)±\sqrt{3969}}{2\left(-49\right)}$$

Tuhia te pūtakerua o te 3969.

$$t=\frac{-\left(-35\right)±63}{2\left(-49\right)}$$

Ko te tauaro o -35 ko 35.

$$t=\frac{35±63}{2\left(-49\right)}$$

Whakareatia 2 ki te -49.

$$t=\frac{35±63}{-98}$$

Nā, me whakaoti te whārite t=\frac{35±63}{-98} ina he tāpiri te ±. Tāpiri 35 ki te 63.

$$t=\frac{98}{-98}$$

Whakawehe 98 ki te -98.

$$t=-1$$

Nā, me whakaoti te whārite t=\frac{35±63}{-98} ina he tango te ±. Tango 63 mai i 35.

$$t=-\frac{28}{-98}$$

Whakahekea te hautanga \frac{-28}{-98} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$t=\frac{2}{7}$$

Kua oti te whārite te whakatau.

$$t=-1 t=\frac{2}{7}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te \frac{1}{2} ki te 98, ka 49.

$$-35t-49t^{2}=-14$$

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.

$$-49t^{2}-35t=-14$$

Whakawehea ngā taha e rua ki te -49.

$$\frac{-49t^{2}-35t}{-49}=-\frac{14}{-49}$$

Mā te whakawehe ki te -49 ka wetekia te whakareanga ki te -49.

$$t^{2}+\left(-\frac{35}{-49}\right)t=-\frac{14}{-49}$$

Whakahekea te hautanga \frac{-35}{-49} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$t^{2}+\frac{5}{7}t=-\frac{14}{-49}$$

Whakahekea te hautanga \frac{-14}{-49} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$t^{2}+\frac{5}{7}t=\frac{2}{7}$$

Whakawehea te \frac{5}{7}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{14}. Nā, tāpiria te pūrua o te \frac{5}{14} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}+\frac{5}{7}t+\left(\frac{5}{14}\right)^{2}=\frac{2}{7}+\left(\frac{5}{14}\right)^{2}$$

Pūruatia \frac{5}{14} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}+\frac{5}{7}t+\frac{25}{196}=\frac{2}{7}+\frac{25}{196}$$

Tāpiri \frac{2}{7} ki te \frac{25}{196} 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.

$$t^{2}+\frac{5}{7}t+\frac{25}{196}=\frac{81}{196}$$

Tauwehea t^{2}+\frac{5}{7}t+\frac{25}{196}. 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}.

$$\left(t+\frac{5}{14}\right)^{2}=\frac{81}{196}$$

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

$$\sqrt{\left(t+\frac{5}{14}\right)^{2}}=\sqrt{\frac{81}{196}}$$

Whakarūnātia.

$$t+\frac{5}{14}=\frac{9}{14} t+\frac{5}{14}=-\frac{9}{14}$$

Me tango \frac{5}{14} mai i ngā taha e rua o te whārite.

$$t=\frac{2}{7} t=-1$$