Whakaoti i te b^2-16b=36

$$b ^ { 2 } - 16 b = 36$$

Whakaoti mō b

$$b=-2$$

$$b=18$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 36 mai i ngā taha e rua.

$$b^{2}-16b-36=0$$

Hei whakaoti i te whārite, whakatauwehea te b^{2}-16b-36 mā te whakamahi i te tātai b^{2}+\left(a+b\right)b+ab=\left(b+a\right)\left(b+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-16 ab=-36$$

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 -36.

$$1,-36 2,-18 3,-12 4,-9 6,-6$$

Tātaihia te tapeke mō ia takirua.

$$1-36=-35 2-18=-16 3-12=-9 4-9=-5 6-6=0$$

Ko te otinga te takirua ka hoatu i te tapeke -16.

$$a=-18 b=2$$

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

$$\left(b-18\right)\left(b+2\right)$$

Hei kimi otinga whārite, me whakaoti te b-18=0 me te b+2=0.

$$b=18 b=-2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 36 mai i ngā taha e rua.

$$b^{2}-16b-36=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei b^{2}+ab+bb-36. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-16 ab=1\left(-36\right)=-36$$

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 -36.

$$1,-36 2,-18 3,-12 4,-9 6,-6$$

Tātaihia te tapeke mō ia takirua.

$$1-36=-35 2-18=-16 3-12=-9 4-9=-5 6-6=0$$

Ko te otinga te takirua ka hoatu i te tapeke -16.

$$a=-18 b=2$$

Tuhia anō te b^{2}-16b-36 hei \left(b^{2}-18b\right)+\left(2b-36\right).

$$\left(b^{2}-18b\right)+\left(2b-36\right)$$

Tauwehea te b i te tuatahi me te 2 i te rōpū tuarua.

$$b\left(b-18\right)+2\left(b-18\right)$$

Whakatauwehea atu te kīanga pātahi b-18 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(b-18\right)\left(b+2\right)$$

Hei kimi otinga whārite, me whakaoti te b-18=0 me te b+2=0.

$$b=18 b=-2$$

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.

$$b^{2}-16b=36$$

Me tango 36 mai i ngā taha e rua o te whārite.

$$b^{2}-16b-36=36-36$$

Mā te tango i te 36 i a ia ake anō ka toe ko te 0.

$$b^{2}-16b-36=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -16 mō b, me -36 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-36\right)}}{2}$$

Pūrua -16.

$$b=\frac{-\left(-16\right)±\sqrt{256-4\left(-36\right)}}{2}$$

Whakareatia -4 ki te -36.

$$b=\frac{-\left(-16\right)±\sqrt{256+144}}{2}$$

Tāpiri 256 ki te 144.

$$b=\frac{-\left(-16\right)±\sqrt{400}}{2}$$

Tuhia te pūtakerua o te 400.

$$b=\frac{-\left(-16\right)±20}{2}$$

Ko te tauaro o -16 ko 16.

$$b=\frac{16±20}{2}$$

Nā, me whakaoti te whārite b=\frac{16±20}{2} ina he tāpiri te ±. Tāpiri 16 ki te 20.

$$b=\frac{36}{2}$$

Whakawehe 36 ki te 2.

$$b=18$$

Nā, me whakaoti te whārite b=\frac{16±20}{2} ina he tango te ±. Tango 20 mai i 16.

$$b=-\frac{4}{2}$$

Whakawehe -4 ki te 2.

$$b=-2$$

Kua oti te whārite te whakatau.

$$b=18 b=-2$$

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.

$$b^{2}-16b=36$$

Whakawehea te -16, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -8. Nā, tāpiria te pūrua o te -8 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$b^{2}-16b+\left(-8\right)^{2}=36+\left(-8\right)^{2}$$

Pūrua -8.

$$b^{2}-16b+64=36+64$$

Tāpiri 36 ki te 64.

$$b^{2}-16b+64=100$$

Tauwehea b^{2}-16b+64. 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}.

$$\left(b-8\right)^{2}=100$$

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

$$\sqrt{\left(b-8\right)^{2}}=\sqrt{100}$$

Whakarūnātia.

$$b-8=10 b-8=-10$$

Me tāpiri 8 ki ngā taha e rua o te whārite.

$$b=18 b=-2$$