Whakaoti i te b^2+12(5-b)=0

$$b ^ { 2 } + 12 ( 5 - b ) = 0$$

Whakaoti mō b

$$b=6+2\sqrt{6}i\approx 6+4.898979486i$$

$$b=-2\sqrt{6}i+6\approx 6-4.898979486i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 12 ki te 5-b.

$$b^{2}+60-12b=0$$

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.

$$b^{2}-12b+60=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -12 mō b, me 60 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 60}}{2}$$

Pūrua -12.

$$b=\frac{-\left(-12\right)±\sqrt{144-4\times 60}}{2}$$

Whakareatia -4 ki te 60.

$$b=\frac{-\left(-12\right)±\sqrt{144-240}}{2}$$

Tāpiri 144 ki te -240.

$$b=\frac{-\left(-12\right)±\sqrt{-96}}{2}$$

Tuhia te pūtakerua o te -96.

$$b=\frac{-\left(-12\right)±4\sqrt{6}i}{2}$$

Ko te tauaro o -12 ko 12.

$$b=\frac{12±4\sqrt{6}i}{2}$$

Nā, me whakaoti te whārite b=\frac{12±4\sqrt{6}i}{2} ina he tāpiri te ±. Tāpiri 12 ki te 4i\sqrt{6}.

$$b=\frac{12+4\sqrt{6}i}{2}$$

Whakawehe 12+4i\sqrt{6} ki te 2.

$$b=6+2\sqrt{6}i$$

Nā, me whakaoti te whārite b=\frac{12±4\sqrt{6}i}{2} ina he tango te ±. Tango 4i\sqrt{6} mai i 12.

$$b=\frac{-4\sqrt{6}i+12}{2}$$

Whakawehe 12-4i\sqrt{6} ki te 2.

$$b=-2\sqrt{6}i+6$$

Kua oti te whārite te whakatau.

$$b=6+2\sqrt{6}i b=-2\sqrt{6}i+6$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 12 ki te 5-b.

$$b^{2}+60-12b=0$$

Tangohia te 60 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$b^{2}-12b=-60$$

Whakawehea te -12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -6. Nā, tāpiria te pūrua o te -6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$b^{2}-12b+\left(-6\right)^{2}=-60+\left(-6\right)^{2}$$

Pūrua -6.

$$b^{2}-12b+36=-60+36$$

Tāpiri -60 ki te 36.

$$b^{2}-12b+36=-24$$

Tauwehea b^{2}-12b+36. 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}.

$$\left(b-6\right)^{2}=-24$$

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

$$\sqrt{\left(b-6\right)^{2}}=\sqrt{-24}$$

Whakarūnātia.

$$b-6=2\sqrt{6}i b-6=-2\sqrt{6}i$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$b=6+2\sqrt{6}i b=-2\sqrt{6}i+6$$