Whakaoti i te b^2+2b=-20

$$b ^ { 2 } + 2 b = - 20$$

Whakaoti mō b

$$b=-1+\sqrt{19}i\approx -1+4.358898944i$$

$$b=-\sqrt{19}i-1\approx -1-4.358898944i$$

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.

$$b^{2}+2b=-20$$

Me tāpiri 20 ki ngā taha e rua o te whārite.

$$b^{2}+2b-\left(-20\right)=-20-\left(-20\right)$$

Mā te tango i te -20 i a ia ake anō ka toe ko te 0.

$$b^{2}+2b-\left(-20\right)=0$$

Tango -20 mai i 0.

$$b^{2}+2b+20=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me 20 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-2±\sqrt{2^{2}-4\times 20}}{2}$$

Pūrua 2.

$$b=\frac{-2±\sqrt{4-4\times 20}}{2}$$

Whakareatia -4 ki te 20.

$$b=\frac{-2±\sqrt{4-80}}{2}$$

Tāpiri 4 ki te -80.

$$b=\frac{-2±\sqrt{-76}}{2}$$

Tuhia te pūtakerua o te -76.

$$b=\frac{-2±2\sqrt{19}i}{2}$$

Nā, me whakaoti te whārite b=\frac{-2±2\sqrt{19}i}{2} ina he tāpiri te ±. Tāpiri -2 ki te 2i\sqrt{19}.

$$b=\frac{-2+2\sqrt{19}i}{2}$$

Whakawehe -2+2i\sqrt{19} ki te 2.

$$b=-1+\sqrt{19}i$$

Nā, me whakaoti te whārite b=\frac{-2±2\sqrt{19}i}{2} ina he tango te ±. Tango 2i\sqrt{19} mai i -2.

$$b=\frac{-2\sqrt{19}i-2}{2}$$

Whakawehe -2-2i\sqrt{19} ki te 2.

$$b=-\sqrt{19}i-1$$

Kua oti te whārite te whakatau.

$$b=-1+\sqrt{19}i b=-\sqrt{19}i-1$$

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.

$$b^{2}+2b=-20$$

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.

$$b^{2}+2b+1^{2}=-20+1^{2}$$

Pūrua 1.

$$b^{2}+2b+1=-20+1$$

Tāpiri -20 ki te 1.

$$b^{2}+2b+1=-19$$

Tauwehea b^{2}+2b+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}.

$$\left(b+1\right)^{2}=-19$$

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

$$\sqrt{\left(b+1\right)^{2}}=\sqrt{-19}$$

Whakarūnātia.

$$b+1=\sqrt{19}i b+1=-\sqrt{19}i$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$b=-1+\sqrt{19}i b=-\sqrt{19}i-1$$