Whakaoti i te 11x^2-54x-192

$$11 { x }^{ 2 } -54x-192$$

Tauwehe

$$11\left(x-\frac{27-\sqrt{2841}}{11}\right)\left(x-\frac{\sqrt{2841}+27}{11}\right)$$

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.

$$11x^{2}-54x-192=0$$

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.

$$x=\frac{-\left(-54\right)±\sqrt{\left(-54\right)^{2}-4\times 11\left(-192\right)}}{2\times 11}$$

Pūrua -54.

$$x=\frac{-\left(-54\right)±\sqrt{2916-4\times 11\left(-192\right)}}{2\times 11}$$

Whakareatia -4 ki te 11.

$$x=\frac{-\left(-54\right)±\sqrt{2916-44\left(-192\right)}}{2\times 11}$$

Whakareatia -44 ki te -192.

$$x=\frac{-\left(-54\right)±\sqrt{2916+8448}}{2\times 11}$$

Tāpiri 2916 ki te 8448.

$$x=\frac{-\left(-54\right)±\sqrt{11364}}{2\times 11}$$

Tuhia te pūtakerua o te 11364.

$$x=\frac{-\left(-54\right)±2\sqrt{2841}}{2\times 11}$$

Ko te tauaro o -54 ko 54.

$$x=\frac{54±2\sqrt{2841}}{2\times 11}$$

Whakareatia 2 ki te 11.

$$x=\frac{54±2\sqrt{2841}}{22}$$

Nā, me whakaoti te whārite x=\frac{54±2\sqrt{2841}}{22} ina he tāpiri te ±. Tāpiri 54 ki te 2\sqrt{2841}.

$$x=\frac{2\sqrt{2841}+54}{22}$$

Whakawehe 54+2\sqrt{2841} ki te 22.

$$x=\frac{\sqrt{2841}+27}{11}$$

Nā, me whakaoti te whārite x=\frac{54±2\sqrt{2841}}{22} ina he tango te ±. Tango 2\sqrt{2841} mai i 54.

$$x=\frac{54-2\sqrt{2841}}{22}$$

Whakawehe 54-2\sqrt{2841} ki te 22.

$$x=\frac{27-\sqrt{2841}}{11}$$

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{27+\sqrt{2841}}{11} mō te x_{1} me te \frac{27-\sqrt{2841}}{11} mō te x_{2}.

$$11x^{2}-54x-192=11\left(x-\frac{\sqrt{2841}+27}{11}\right)\left(x-\frac{27-\sqrt{2841}}{11}\right)$$

Aromātai

$$11x^{2}-54x-192$$