Whakaoti i te b^2+15b+5b=0

$$b ^ { 2 } + 15 b + 5 b = 0$$

Whakaoti mō b

$$b=-20$$

$$b=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te b.

$$b\left(b+15+5\right)=0$$

Hei kimi otinga whārite, me whakaoti te b=0 me te b+20=0.

$$b=0 b=-20$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 15b me 5b, ka 20b.

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

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

$$b=\frac{-20±\sqrt{20^{2}}}{2}$$

Tuhia te pūtakerua o te 20^{2}.

$$b=\frac{-20±20}{2}$$

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

$$b=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$b=0$$

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

$$b=-\frac{40}{2}$$

Whakawehe -40 ki te 2.

$$b=-20$$

Kua oti te whārite te whakatau.

$$b=0 b=-20$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te 15b me 5b, ka 20b.

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

Whakawehea te 20, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 10. Nā, tāpiria te pūrua o te 10 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$b^{2}+20b+10^{2}=10^{2}$$

Pūrua 10.

$$b^{2}+20b+100=100$$

Tauwehea b^{2}+20b+100. 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}.

$$\left(b+10\right)^{2}=100$$

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

$$\sqrt{\left(b+10\right)^{2}}=\sqrt{100}$$

Whakarūnātia.

$$b+10=10 b+10=-10$$

Me tango 10 mai i ngā taha e rua o te whārite.

$$b=0 b=-20$$