Whakaoti i te 9x^2+1x-97

$$9 x ^ { 2 } + 1 x - 97$$

Tauwehe

$$9\left(x-\frac{-\sqrt{3493}-1}{18}\right)\left(x-\frac{\sqrt{3493}-1}{18}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$9x^{2}+x-97=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\times 9\left(-97\right)}}{2\times 9}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\times 9\left(-97\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-1±\sqrt{1-36\left(-97\right)}}{2\times 9}$$

Whakareatia -36 ki te -97.

$$x=\frac{-1±\sqrt{1+3492}}{2\times 9}$$

Tāpiri 1 ki te 3492.

$$x=\frac{-1±\sqrt{3493}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{-1±\sqrt{3493}}{18}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{3493}}{18} ina he tāpiri te ±. Tāpiri -1 ki te \sqrt{3493}.

$$x=\frac{\sqrt{3493}-1}{18}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{3493}}{18} ina he tango te ±. Tango \sqrt{3493} mai i -1.

$$x=\frac{-\sqrt{3493}-1}{18}$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{-1+\sqrt{3493}}{18} mō te x_{1} me te \frac{-1-\sqrt{3493}}{18} mō te x_{2}.

$$9x^{2}+x-97=9\left(x-\frac{\sqrt{3493}-1}{18}\right)\left(x-\frac{-\sqrt{3493}-1}{18}\right)$$

Aromātai

$$9x^{2}+x-97$$