Whakaoti i te 84j=-7j^2

$$84 j = - 7 j ^ { 2 }$$

Whakaoti mō j

$$j=-12$$

$$j=0$$

Ngā Upane Whakamahi Tauwehe

Me tāpiri te 7j^{2} ki ngā taha e rua.

$$84j+7j^{2}=0$$

Tauwehea te j.

$$j\left(84+7j\right)=0$$

Hei kimi otinga whārite, me whakaoti te j=0 me te 84+7j=0.

$$j=0 j=-12$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 7j^{2} ki ngā taha e rua.

$$84j+7j^{2}=0$$

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.

$$7j^{2}+84j=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 7 mō a, 84 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$j=\frac{-84±\sqrt{84^{2}}}{2\times 7}$$

Tuhia te pūtakerua o te 84^{2}.

$$j=\frac{-84±84}{2\times 7}$$

Whakareatia 2 ki te 7.

$$j=\frac{-84±84}{14}$$

Nā, me whakaoti te whārite j=\frac{-84±84}{14} ina he tāpiri te ±. Tāpiri -84 ki te 84.

$$j=\frac{0}{14}$$

Whakawehe 0 ki te 14.

$$j=0$$

Nā, me whakaoti te whārite j=\frac{-84±84}{14} ina he tango te ±. Tango 84 mai i -84.

$$j=-\frac{168}{14}$$

Whakawehe -168 ki te 14.

$$j=-12$$

Kua oti te whārite te whakatau.

$$j=0 j=-12$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 7j^{2} ki ngā taha e rua.

$$84j+7j^{2}=0$$

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.

$$7j^{2}+84j=0$$

Whakawehea ngā taha e rua ki te 7.

$$\frac{7j^{2}+84j}{7}=\frac{0}{7}$$

Mā te whakawehe ki te 7 ka wetekia te whakareanga ki te 7.

$$j^{2}+\frac{84}{7}j=\frac{0}{7}$$

Whakawehe 84 ki te 7.

$$j^{2}+12j=\frac{0}{7}$$

Whakawehe 0 ki te 7.

$$j^{2}+12j=0$$

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.

$$j^{2}+12j+6^{2}=6^{2}$$

Pūrua 6.

$$j^{2}+12j+36=36$$

Tauwehea j^{2}+12j+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}.

$$\left(j+6\right)^{2}=36$$

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

$$\sqrt{\left(j+6\right)^{2}}=\sqrt{36}$$

Whakarūnātia.

$$j+6=6 j+6=-6$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$j=0 j=-12$$