Whakaoti i te 48x^2+240x-1800

$$48 x ^ { 2 } + 240 x - 1800$$

Tauwehe

$$48\left(x-\frac{-5\sqrt{7}-5}{2}\right)\left(x-\frac{5\sqrt{7}-5}{2}\right)$$

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.

$$48x^{2}+240x-1800=0$$

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.

$$x=\frac{-240±\sqrt{240^{2}-4\times 48\left(-1800\right)}}{2\times 48}$$

Pūrua 240.

$$x=\frac{-240±\sqrt{57600-4\times 48\left(-1800\right)}}{2\times 48}$$

Whakareatia -4 ki te 48.

$$x=\frac{-240±\sqrt{57600-192\left(-1800\right)}}{2\times 48}$$

Whakareatia -192 ki te -1800.

$$x=\frac{-240±\sqrt{57600+345600}}{2\times 48}$$

Tāpiri 57600 ki te 345600.

$$x=\frac{-240±\sqrt{403200}}{2\times 48}$$

Tuhia te pūtakerua o te 403200.

$$x=\frac{-240±240\sqrt{7}}{2\times 48}$$

Whakareatia 2 ki te 48.

$$x=\frac{-240±240\sqrt{7}}{96}$$

Nā, me whakaoti te whārite x=\frac{-240±240\sqrt{7}}{96} ina he tāpiri te ±. Tāpiri -240 ki te 240\sqrt{7}.

$$x=\frac{240\sqrt{7}-240}{96}$$

Whakawehe -240+240\sqrt{7} ki te 96.

$$x=\frac{5\sqrt{7}-5}{2}$$

Nā, me whakaoti te whārite x=\frac{-240±240\sqrt{7}}{96} ina he tango te ±. Tango 240\sqrt{7} mai i -240.

$$x=\frac{-240\sqrt{7}-240}{96}$$

Whakawehe -240-240\sqrt{7} ki te 96.

$$x=\frac{-5\sqrt{7}-5}{2}$$

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{-5+5\sqrt{7}}{2} mō te x_{1} me te \frac{-5-5\sqrt{7}}{2} mō te x_{2}.

$$48x^{2}+240x-1800=48\left(x-\frac{5\sqrt{7}-5}{2}\right)\left(x-\frac{-5\sqrt{7}-5}{2}\right)$$

Aromātai

$$48x^{2}+240x-1800$$