Whakaoti i te 16x^2+x-75

$$16 { x }^{ 2 } +x-75$$

Tauwehe

$$16\left(x-\frac{-\sqrt{4801}-1}{32}\right)\left(x-\frac{\sqrt{4801}-1}{32}\right)$$

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.

$$16x^{2}+x-75=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\times 16\left(-75\right)}}{2\times 16}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\times 16\left(-75\right)}}{2\times 16}$$

Whakareatia -4 ki te 16.

$$x=\frac{-1±\sqrt{1-64\left(-75\right)}}{2\times 16}$$

Whakareatia -64 ki te -75.

$$x=\frac{-1±\sqrt{1+4800}}{2\times 16}$$

Tāpiri 1 ki te 4800.

$$x=\frac{-1±\sqrt{4801}}{2\times 16}$$

Whakareatia 2 ki te 16.

$$x=\frac{-1±\sqrt{4801}}{32}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{4801}}{32} ina he tāpiri te ±. Tāpiri -1 ki te \sqrt{4801}.

$$x=\frac{\sqrt{4801}-1}{32}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{4801}}{32} ina he tango te ±. Tango \sqrt{4801} mai i -1.

$$x=\frac{-\sqrt{4801}-1}{32}$$

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{4801}}{32} mō te x_{1} me te \frac{-1-\sqrt{4801}}{32} mō te x_{2}.

$$16x^{2}+x-75=16\left(x-\frac{\sqrt{4801}-1}{32}\right)\left(x-\frac{-\sqrt{4801}-1}{32}\right)$$

Aromātai

$$16x^{2}+x-75$$