Whakaoti i te x^2-156x-320

$$x ^ { 2 } - 156 x - 320$$

Tauwehe

$$\left(x-\left(78-2\sqrt{1601}\right)\right)\left(x-\left(2\sqrt{1601}+78\right)\right)$$

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.

$$x^{2}-156x-320=0$$

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.

$$x=\frac{-\left(-156\right)±\sqrt{\left(-156\right)^{2}-4\left(-320\right)}}{2}$$

Pūrua -156.

$$x=\frac{-\left(-156\right)±\sqrt{24336-4\left(-320\right)}}{2}$$

Whakareatia -4 ki te -320.

$$x=\frac{-\left(-156\right)±\sqrt{24336+1280}}{2}$$

Tāpiri 24336 ki te 1280.

$$x=\frac{-\left(-156\right)±\sqrt{25616}}{2}$$

Tuhia te pūtakerua o te 25616.

$$x=\frac{-\left(-156\right)±4\sqrt{1601}}{2}$$

Ko te tauaro o -156 ko 156.

$$x=\frac{156±4\sqrt{1601}}{2}$$

Nā, me whakaoti te whārite x=\frac{156±4\sqrt{1601}}{2} ina he tāpiri te ±. Tāpiri 156 ki te 4\sqrt{1601}.

$$x=\frac{4\sqrt{1601}+156}{2}$$

Whakawehe 156+4\sqrt{1601} ki te 2.

$$x=2\sqrt{1601}+78$$

Nā, me whakaoti te whārite x=\frac{156±4\sqrt{1601}}{2} ina he tango te ±. Tango 4\sqrt{1601} mai i 156.

$$x=\frac{156-4\sqrt{1601}}{2}$$

Whakawehe 156-4\sqrt{1601} ki te 2.

$$x=78-2\sqrt{1601}$$

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 78+2\sqrt{1601} mō te x_{1} me te 78-2\sqrt{1601} mō te x_{2}.

$$x^{2}-156x-320=\left(x-\left(2\sqrt{1601}+78\right)\right)\left(x-\left(78-2\sqrt{1601}\right)\right)$$

Aromātai

$$x^{2}-156x-320$$