Whakaoti i te -4x^2+133x-63

$$- 4 x ^ { 2 } + 133 x - 63$$

Tauwehe

$$-4\left(x-\frac{133-\sqrt{16681}}{8}\right)\left(x-\frac{\sqrt{16681}+133}{8}\right)$$

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.

$$-4x^{2}+133x-63=0$$

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.

$$x=\frac{-133±\sqrt{133^{2}-4\left(-4\right)\left(-63\right)}}{2\left(-4\right)}$$

Pūrua 133.

$$x=\frac{-133±\sqrt{17689-4\left(-4\right)\left(-63\right)}}{2\left(-4\right)}$$

Whakareatia -4 ki te -4.

$$x=\frac{-133±\sqrt{17689+16\left(-63\right)}}{2\left(-4\right)}$$

Whakareatia 16 ki te -63.

$$x=\frac{-133±\sqrt{17689-1008}}{2\left(-4\right)}$$

Tāpiri 17689 ki te -1008.

$$x=\frac{-133±\sqrt{16681}}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{-133±\sqrt{16681}}{-8}$$

Nā, me whakaoti te whārite x=\frac{-133±\sqrt{16681}}{-8} ina he tāpiri te ±. Tāpiri -133 ki te \sqrt{16681}.

$$x=\frac{\sqrt{16681}-133}{-8}$$

Whakawehe -133+\sqrt{16681} ki te -8.

$$x=\frac{133-\sqrt{16681}}{8}$$

Nā, me whakaoti te whārite x=\frac{-133±\sqrt{16681}}{-8} ina he tango te ±. Tango \sqrt{16681} mai i -133.

$$x=\frac{-\sqrt{16681}-133}{-8}$$

Whakawehe -133-\sqrt{16681} ki te -8.

$$x=\frac{\sqrt{16681}+133}{8}$$

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{133-\sqrt{16681}}{8} mō te x_{1} me te \frac{133+\sqrt{16681}}{8} mō te x_{2}.

$$-4x^{2}+133x-63=-4\left(x-\frac{133-\sqrt{16681}}{8}\right)\left(x-\frac{\sqrt{16681}+133}{8}\right)$$

Aromātai

$$-4x^{2}+133x-63$$