Whakaoti i te 12b^2-b+324=0

$$12 b ^ { 2 } - b + 324 = 0$$

Whakaoti mō b

$$b=\frac{1+\sqrt{15551}i}{24}\approx 0.041666667+5.195985363i$$

$$b=\frac{-\sqrt{15551}i+1}{24}\approx 0.041666667-5.195985363i$$

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.

$$12b^{2}-b+324=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 12 mō a, -1 mō b, me 324 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-\left(-1\right)±\sqrt{1-4\times 12\times 324}}{2\times 12}$$

Whakareatia -4 ki te 12.

$$b=\frac{-\left(-1\right)±\sqrt{1-48\times 324}}{2\times 12}$$

Whakareatia -48 ki te 324.

$$b=\frac{-\left(-1\right)±\sqrt{1-15552}}{2\times 12}$$

Tāpiri 1 ki te -15552.

$$b=\frac{-\left(-1\right)±\sqrt{-15551}}{2\times 12}$$

Tuhia te pūtakerua o te -15551.

$$b=\frac{-\left(-1\right)±\sqrt{15551}i}{2\times 12}$$

Ko te tauaro o -1 ko 1.

$$b=\frac{1±\sqrt{15551}i}{2\times 12}$$

Whakareatia 2 ki te 12.

$$b=\frac{1±\sqrt{15551}i}{24}$$

Nā, me whakaoti te whārite b=\frac{1±\sqrt{15551}i}{24} ina he tāpiri te ±. Tāpiri 1 ki te i\sqrt{15551}.

$$b=\frac{1+\sqrt{15551}i}{24}$$

Nā, me whakaoti te whārite b=\frac{1±\sqrt{15551}i}{24} ina he tango te ±. Tango i\sqrt{15551} mai i 1.

$$b=\frac{-\sqrt{15551}i+1}{24}$$

Kua oti te whārite te whakatau.

$$b=\frac{1+\sqrt{15551}i}{24} b=\frac{-\sqrt{15551}i+1}{24}$$

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.

$$12b^{2}-b+324=0$$

Me tango 324 mai i ngā taha e rua o te whārite.

$$12b^{2}-b+324-324=-324$$

Mā te tango i te 324 i a ia ake anō ka toe ko te 0.

$$12b^{2}-b=-324$$

Whakawehea ngā taha e rua ki te 12.

$$\frac{12b^{2}-b}{12}=-\frac{324}{12}$$

Mā te whakawehe ki te 12 ka wetekia te whakareanga ki te 12.

$$b^{2}-\frac{1}{12}b=-\frac{324}{12}$$

Whakawehe -324 ki te 12.

$$b^{2}-\frac{1}{12}b=-27$$

Whakawehea te -\frac{1}{12}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{24}. Nā, tāpiria te pūrua o te -\frac{1}{24} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$b^{2}-\frac{1}{12}b+\left(-\frac{1}{24}\right)^{2}=-27+\left(-\frac{1}{24}\right)^{2}$$

Pūruatia -\frac{1}{24} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$b^{2}-\frac{1}{12}b+\frac{1}{576}=-27+\frac{1}{576}$$

Tāpiri -27 ki te \frac{1}{576}.

$$b^{2}-\frac{1}{12}b+\frac{1}{576}=-\frac{15551}{576}$$

Tauwehea b^{2}-\frac{1}{12}b+\frac{1}{576}. 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}.

$$\left(b-\frac{1}{24}\right)^{2}=-\frac{15551}{576}$$

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

$$\sqrt{\left(b-\frac{1}{24}\right)^{2}}=\sqrt{-\frac{15551}{576}}$$

Whakarūnātia.

$$b-\frac{1}{24}=\frac{\sqrt{15551}i}{24} b-\frac{1}{24}=-\frac{\sqrt{15551}i}{24}$$

Me tāpiri \frac{1}{24} ki ngā taha e rua o te whārite.

$$b=\frac{1+\sqrt{15551}i}{24} b=\frac{-\sqrt{15551}i+1}{24}$$