Whakaoti i te 2b^2+2b-12=0

$$2 b ^ { 2 } + 2 b - 12 = 0$$

Whakaoti mō b

$$b=-3$$

$$b=2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakawehea ngā taha e rua ki te 2.

$$b^{2}+b-6=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei b^{2}+ab+bb-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=1\left(-6\right)=-6$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -6.

$$-1,6 -2,3$$

Tātaihia te tapeke mō ia takirua.

$$-1+6=5 -2+3=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=-2 b=3$$

Tuhia anō te b^{2}+b-6 hei \left(b^{2}-2b\right)+\left(3b-6\right).

$$\left(b^{2}-2b\right)+\left(3b-6\right)$$

Tauwehea te b i te tuatahi me te 3 i te rōpū tuarua.

$$b\left(b-2\right)+3\left(b-2\right)$$

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

$$\left(b-2\right)\left(b+3\right)$$

Hei kimi otinga whārite, me whakaoti te b-2=0 me te b+3=0.

$$b=2 b=-3$$

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.

$$2b^{2}+2b-12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 2 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-2±\sqrt{2^{2}-4\times 2\left(-12\right)}}{2\times 2}$$

Pūrua 2.

$$b=\frac{-2±\sqrt{4-4\times 2\left(-12\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$b=\frac{-2±\sqrt{4-8\left(-12\right)}}{2\times 2}$$

Whakareatia -8 ki te -12.

$$b=\frac{-2±\sqrt{4+96}}{2\times 2}$$

Tāpiri 4 ki te 96.

$$b=\frac{-2±\sqrt{100}}{2\times 2}$$

Tuhia te pūtakerua o te 100.

$$b=\frac{-2±10}{2\times 2}$$

Whakareatia 2 ki te 2.

$$b=\frac{-2±10}{4}$$

Nā, me whakaoti te whārite b=\frac{-2±10}{4} ina he tāpiri te ±. Tāpiri -2 ki te 10.

$$b=\frac{8}{4}$$

Whakawehe 8 ki te 4.

$$b=2$$

Nā, me whakaoti te whārite b=\frac{-2±10}{4} ina he tango te ±. Tango 10 mai i -2.

$$b=-\frac{12}{4}$$

Whakawehe -12 ki te 4.

$$b=-3$$

Kua oti te whārite te whakatau.

$$b=2 b=-3$$

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.

$$2b^{2}+2b-12=0$$

Me tāpiri 12 ki ngā taha e rua o te whārite.

$$2b^{2}+2b-12-\left(-12\right)=-\left(-12\right)$$

Mā te tango i te -12 i a ia ake anō ka toe ko te 0.

$$2b^{2}+2b=-\left(-12\right)$$

Tango -12 mai i 0.

$$2b^{2}+2b=12$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2b^{2}+2b}{2}=\frac{12}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$b^{2}+\frac{2}{2}b=\frac{12}{2}$$

Whakawehe 2 ki te 2.

$$b^{2}+b=\frac{12}{2}$$

Whakawehe 12 ki te 2.

$$b^{2}+b=6$$

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

$$b^{2}+b+\left(\frac{1}{2}\right)^{2}=6+\left(\frac{1}{2}\right)^{2}$$

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$b^{2}+b+\frac{1}{4}=6+\frac{1}{4}$$

Tāpiri 6 ki te \frac{1}{4}.

$$b^{2}+b+\frac{1}{4}=\frac{25}{4}$$

Tauwehea b^{2}+b+\frac{1}{4}. 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}.

$$\left(b+\frac{1}{2}\right)^{2}=\frac{25}{4}$$

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

$$\sqrt{\left(b+\frac{1}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Whakarūnātia.

$$b+\frac{1}{2}=\frac{5}{2} b+\frac{1}{2}=-\frac{5}{2}$$

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$b=2 b=-3$$