Whakaoti i te x^2+30x-120

$${ x }^{ 2 } +30x-120$$

Tauwehe

$$\left(x-\left(-\sqrt{345}-15\right)\right)\left(x-\left(\sqrt{345}-15\right)\right)$$

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.

$$x^{2}+30x-120=0$$

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.

$$x=\frac{-30±\sqrt{30^{2}-4\left(-120\right)}}{2}$$

Pūrua 30.

$$x=\frac{-30±\sqrt{900-4\left(-120\right)}}{2}$$

Whakareatia -4 ki te -120.

$$x=\frac{-30±\sqrt{900+480}}{2}$$

Tāpiri 900 ki te 480.

$$x=\frac{-30±\sqrt{1380}}{2}$$

Tuhia te pūtakerua o te 1380.

$$x=\frac{-30±2\sqrt{345}}{2}$$

Nā, me whakaoti te whārite x=\frac{-30±2\sqrt{345}}{2} ina he tāpiri te ±. Tāpiri -30 ki te 2\sqrt{345}.

$$x=\frac{2\sqrt{345}-30}{2}$$

Whakawehe -30+2\sqrt{345} ki te 2.

$$x=\sqrt{345}-15$$

Nā, me whakaoti te whārite x=\frac{-30±2\sqrt{345}}{2} ina he tango te ±. Tango 2\sqrt{345} mai i -30.

$$x=\frac{-2\sqrt{345}-30}{2}$$

Whakawehe -30-2\sqrt{345} ki te 2.

$$x=-\sqrt{345}-15$$

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 -15+\sqrt{345} mō te x_{1} me te -15-\sqrt{345} mō te x_{2}.

$$x^{2}+30x-120=\left(x-\left(\sqrt{345}-15\right)\right)\left(x-\left(-\sqrt{345}-15\right)\right)$$

Aromātai

$$x^{2}+30x-120$$