Whakaoti i te 7x^2+12x-420

$$7 x ^ { 2 } + 12 x - 420$$

Tauwehe

$$7\left(x-\frac{-4\sqrt{186}-6}{7}\right)\left(x-\frac{4\sqrt{186}-6}{7}\right)$$

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.

$$7x^{2}+12x-420=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 7\left(-420\right)}}{2\times 7}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 7\left(-420\right)}}{2\times 7}$$

Whakareatia -4 ki te 7.

$$x=\frac{-12±\sqrt{144-28\left(-420\right)}}{2\times 7}$$

Whakareatia -28 ki te -420.

$$x=\frac{-12±\sqrt{144+11760}}{2\times 7}$$

Tāpiri 144 ki te 11760.

$$x=\frac{-12±\sqrt{11904}}{2\times 7}$$

Tuhia te pūtakerua o te 11904.

$$x=\frac{-12±8\sqrt{186}}{2\times 7}$$

Whakareatia 2 ki te 7.

$$x=\frac{-12±8\sqrt{186}}{14}$$

Nā, me whakaoti te whārite x=\frac{-12±8\sqrt{186}}{14} ina he tāpiri te ±. Tāpiri -12 ki te 8\sqrt{186}.

$$x=\frac{8\sqrt{186}-12}{14}$$

Whakawehe -12+8\sqrt{186} ki te 14.

$$x=\frac{4\sqrt{186}-6}{7}$$

Nā, me whakaoti te whārite x=\frac{-12±8\sqrt{186}}{14} ina he tango te ±. Tango 8\sqrt{186} mai i -12.

$$x=\frac{-8\sqrt{186}-12}{14}$$

Whakawehe -12-8\sqrt{186} ki te 14.

$$x=\frac{-4\sqrt{186}-6}{7}$$

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{-6+4\sqrt{186}}{7} mō te x_{1} me te \frac{-6-4\sqrt{186}}{7} mō te x_{2}.

$$7x^{2}+12x-420=7\left(x-\frac{4\sqrt{186}-6}{7}\right)\left(x-\frac{-4\sqrt{186}-6}{7}\right)$$

Aromātai

$$7x^{2}+12x-420$$