Whakaoti i te v^2-35=2v

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

Whakaoti mō v

$$v=-5$$

$$v=7$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 2v mai i ngā taha e rua.

$$v^{2}-35-2v=0$$

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

$$v^{2}-2v-35=0$$

Hei whakaoti i te whārite, whakatauwehea te v^{2}-2v-35 mā te whakamahi i te tātai v^{2}+\left(a+b\right)v+ab=\left(v+a\right)\left(v+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=-35$$

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 -35.

$$1,-35 5,-7$$

Tātaihia te tapeke mō ia takirua.

$$1-35=-34 5-7=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -2.

$$a=-7 b=5$$

Me tuhi anō te kīanga whakatauwehe \left(v+a\right)\left(v+b\right) mā ngā uara i tātaihia.

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

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

$$v=7 v=-5$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 2v mai i ngā taha e rua.

$$v^{2}-35-2v=0$$

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

$$v^{2}-2v-35=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei v^{2}+av+bv-35. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=1\left(-35\right)=-35$$

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 -35.

$$1,-35 5,-7$$

Tātaihia te tapeke mō ia takirua.

$$1-35=-34 5-7=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -2.

$$a=-7 b=5$$

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

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

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

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

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

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

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

$$v=7 v=-5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 2v mai i ngā taha e rua.

$$v^{2}-35-2v=0$$

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.

$$v^{2}-2v-35=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -35 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-35\right)}}{2}$$

Pūrua -2.

$$v=\frac{-\left(-2\right)±\sqrt{4-4\left(-35\right)}}{2}$$

Whakareatia -4 ki te -35.

$$v=\frac{-\left(-2\right)±\sqrt{4+140}}{2}$$

Tāpiri 4 ki te 140.

$$v=\frac{-\left(-2\right)±\sqrt{144}}{2}$$

Tuhia te pūtakerua o te 144.

$$v=\frac{-\left(-2\right)±12}{2}$$

Ko te tauaro o -2 ko 2.

$$v=\frac{2±12}{2}$$

Nā, me whakaoti te whārite v=\frac{2±12}{2} ina he tāpiri te ±. Tāpiri 2 ki te 12.

$$v=\frac{14}{2}$$

Whakawehe 14 ki te 2.

$$v=7$$

Nā, me whakaoti te whārite v=\frac{2±12}{2} ina he tango te ±. Tango 12 mai i 2.

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

Whakawehe -10 ki te 2.

$$v=-5$$

Kua oti te whārite te whakatau.

$$v=7 v=-5$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 2v mai i ngā taha e rua.

$$v^{2}-35-2v=0$$

Me tāpiri te 35 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$v^{2}-2v+1=35+1$$

Tāpiri 35 ki te 1.

$$v^{2}-2v+1=36$$

Tauwehea v^{2}-2v+1. 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}.

$$\left(v-1\right)^{2}=36$$

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

$$\sqrt{\left(v-1\right)^{2}}=\sqrt{36}$$

Whakarūnātia.

$$v-1=6 v-1=-6$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$v=7 v=-5$$