Whakaoti i te (v-7)=5v(v-7)

$$( v - 7 ) = 5 v ( v - 7 )$$

Whakaoti mō v

$$v=7$$

$$v=\frac{1}{5}=0.2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakamahia te āhuatanga tohatoha hei whakarea te 5v ki te v-7.

$$v-7=5v^{2}-35v$$

Tangohia te 5v^{2} mai i ngā taha e rua.

$$v-7-5v^{2}=-35v$$

Me tāpiri te 35v ki ngā taha e rua.

$$v-7-5v^{2}+35v=0$$

Pahekotia te v me 35v, ka 36v.

$$36v-7-5v^{2}=0$$

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

$$-5v^{2}+36v-7=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -5v^{2}+av+bv-7. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=36 ab=-5\left(-7\right)=35$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 35.

$$1,35 5,7$$

Tātaihia te tapeke mō ia takirua.

$$1+35=36 5+7=12$$

Ko te otinga te takirua ka hoatu i te tapeke 36.

$$a=35 b=1$$

Tuhia anō te -5v^{2}+36v-7 hei \left(-5v^{2}+35v\right)+\left(v-7\right).

$$\left(-5v^{2}+35v\right)+\left(v-7\right)$$

Tauwehea te 5v i te tuatahi me te -1 i te rōpū tuarua.

$$5v\left(-v+7\right)-\left(-v+7\right)$$

Whakatauwehea atu te kīanga pātahi -v+7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-v+7\right)\left(5v-1\right)$$

Hei kimi otinga whārite, me whakaoti te -v+7=0 me te 5v-1=0.

$$v=7 v=\frac{1}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 5v ki te v-7.

$$v-7=5v^{2}-35v$$

Tangohia te 5v^{2} mai i ngā taha e rua.

$$v-7-5v^{2}=-35v$$

Me tāpiri te 35v ki ngā taha e rua.

$$v-7-5v^{2}+35v=0$$

Pahekotia te v me 35v, ka 36v.

$$36v-7-5v^{2}=0$$

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.

$$-5v^{2}+36v-7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -5 mō a, 36 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{-36±\sqrt{36^{2}-4\left(-5\right)\left(-7\right)}}{2\left(-5\right)}$$

Pūrua 36.

$$v=\frac{-36±\sqrt{1296-4\left(-5\right)\left(-7\right)}}{2\left(-5\right)}$$

Whakareatia -4 ki te -5.

$$v=\frac{-36±\sqrt{1296+20\left(-7\right)}}{2\left(-5\right)}$$

Whakareatia 20 ki te -7.

$$v=\frac{-36±\sqrt{1296-140}}{2\left(-5\right)}$$

Tāpiri 1296 ki te -140.

$$v=\frac{-36±\sqrt{1156}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te 1156.

$$v=\frac{-36±34}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$v=\frac{-36±34}{-10}$$

Nā, me whakaoti te whārite v=\frac{-36±34}{-10} ina he tāpiri te ±. Tāpiri -36 ki te 34.

$$v=-\frac{2}{-10}$$

Whakahekea te hautanga \frac{-2}{-10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$v=\frac{1}{5}$$

Nā, me whakaoti te whārite v=\frac{-36±34}{-10} ina he tango te ±. Tango 34 mai i -36.

$$v=-\frac{70}{-10}$$

Whakawehe -70 ki te -10.

$$v=7$$

Kua oti te whārite te whakatau.

$$v=\frac{1}{5} v=7$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 5v ki te v-7.

$$v-7=5v^{2}-35v$$

Tangohia te 5v^{2} mai i ngā taha e rua.

$$v-7-5v^{2}=-35v$$

Me tāpiri te 35v ki ngā taha e rua.

$$v-7-5v^{2}+35v=0$$

Pahekotia te v me 35v, ka 36v.

$$36v-7-5v^{2}=0$$

Me tāpiri te 7 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$36v-5v^{2}=7$$

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.

$$-5v^{2}+36v=7$$

Whakawehea ngā taha e rua ki te -5.

$$\frac{-5v^{2}+36v}{-5}=\frac{7}{-5}$$

Mā te whakawehe ki te -5 ka wetekia te whakareanga ki te -5.

$$v^{2}+\frac{36}{-5}v=\frac{7}{-5}$$

Whakawehe 36 ki te -5.

$$v^{2}-\frac{36}{5}v=\frac{7}{-5}$$

Whakawehe 7 ki te -5.

$$v^{2}-\frac{36}{5}v=-\frac{7}{5}$$

Whakawehea te -\frac{36}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{18}{5}. Nā, tāpiria te pūrua o te -\frac{18}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$v^{2}-\frac{36}{5}v+\left(-\frac{18}{5}\right)^{2}=-\frac{7}{5}+\left(-\frac{18}{5}\right)^{2}$$

Pūruatia -\frac{18}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$v^{2}-\frac{36}{5}v+\frac{324}{25}=-\frac{7}{5}+\frac{324}{25}$$

Tāpiri -\frac{7}{5} ki te \frac{324}{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.

$$v^{2}-\frac{36}{5}v+\frac{324}{25}=\frac{289}{25}$$

Tauwehea v^{2}-\frac{36}{5}v+\frac{324}{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}.

$$\left(v-\frac{18}{5}\right)^{2}=\frac{289}{25}$$

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

$$\sqrt{\left(v-\frac{18}{5}\right)^{2}}=\sqrt{\frac{289}{25}}$$

Whakarūnātia.

$$v-\frac{18}{5}=\frac{17}{5} v-\frac{18}{5}=-\frac{17}{5}$$

Me tāpiri \frac{18}{5} ki ngā taha e rua o te whārite.

$$v=7 v=\frac{1}{5}$$