Whakaoti i te x^2+600x+32400

$$x ^ { 2 } + 600 x + 32400$$

Tauwehe

$$\left(x+60\right)\left(x+540\right)$$

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.

$$x^{2}+600x+32400=0$$

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.

$$x=\frac{-600±\sqrt{600^{2}-4\times 32400}}{2}$$

Pūrua 600.

$$x=\frac{-600±\sqrt{360000-4\times 32400}}{2}$$

Whakareatia -4 ki te 32400.

$$x=\frac{-600±\sqrt{360000-129600}}{2}$$

Tāpiri 360000 ki te -129600.

$$x=\frac{-600±\sqrt{230400}}{2}$$

Tuhia te pūtakerua o te 230400.

$$x=\frac{-600±480}{2}$$

Nā, me whakaoti te whārite x=\frac{-600±480}{2} ina he tāpiri te ±. Tāpiri -600 ki te 480.

$$x=-\frac{120}{2}$$

Whakawehe -120 ki te 2.

$$x=-60$$

Nā, me whakaoti te whārite x=\frac{-600±480}{2} ina he tango te ±. Tango 480 mai i -600.

$$x=-\frac{1080}{2}$$

Whakawehe -1080 ki te 2.

$$x=-540$$

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 -60 mō te x_{1} me te -540 mō te x_{2}.

$$x^{2}+600x+32400=\left(x-\left(-60\right)\right)\left(x-\left(-540\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$x^{2}+600x+32400=\left(x+60\right)\left(x+540\right)$$

Aromātai

$$\left(x+60\right)\left(x+540\right)$$