Whakaoti i te 2x^2+12x-45

$$2 { x }^{ 2 } +12x-45$$

Tauwehe

$$2\left(x-\left(-\frac{3\sqrt{14}}{2}-3\right)\right)\left(x-\left(\frac{3\sqrt{14}}{2}-3\right)\right)$$

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.

$$2x^{2}+12x-45=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 2\left(-45\right)}}{2\times 2}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 2\left(-45\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-12±\sqrt{144-8\left(-45\right)}}{2\times 2}$$

Whakareatia -8 ki te -45.

$$x=\frac{-12±\sqrt{144+360}}{2\times 2}$$

Tāpiri 144 ki te 360.

$$x=\frac{-12±\sqrt{504}}{2\times 2}$$

Tuhia te pūtakerua o te 504.

$$x=\frac{-12±6\sqrt{14}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-12±6\sqrt{14}}{4}$$

Nā, me whakaoti te whārite x=\frac{-12±6\sqrt{14}}{4} ina he tāpiri te ±. Tāpiri -12 ki te 6\sqrt{14}.

$$x=\frac{6\sqrt{14}-12}{4}$$

Whakawehe -12+6\sqrt{14} ki te 4.

$$x=\frac{3\sqrt{14}}{2}-3$$

Nā, me whakaoti te whārite x=\frac{-12±6\sqrt{14}}{4} ina he tango te ±. Tango 6\sqrt{14} mai i -12.

$$x=\frac{-6\sqrt{14}-12}{4}$$

Whakawehe -12-6\sqrt{14} ki te 4.

$$x=-\frac{3\sqrt{14}}{2}-3$$

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 -3+\frac{3\sqrt{14}}{2} mō te x_{1} me te -3-\frac{3\sqrt{14}}{2} mō te x_{2}.

$$2x^{2}+12x-45=2\left(x-\left(\frac{3\sqrt{14}}{2}-3\right)\right)\left(x-\left(-\frac{3\sqrt{14}}{2}-3\right)\right)$$

Aromātai

$$2x^{2}+12x-45$$