Whakaoti i te 9a^2+42a-49

$$9 a ^ { 2 } + 42 a - 49$$

Tauwehe

$$9\left(a-\frac{-7\sqrt{2}-7}{3}\right)\left(a-\frac{7\sqrt{2}-7}{3}\right)$$

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.

$$9a^{2}+42a-49=0$$

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.

$$a=\frac{-42±\sqrt{42^{2}-4\times 9\left(-49\right)}}{2\times 9}$$

Pūrua 42.

$$a=\frac{-42±\sqrt{1764-4\times 9\left(-49\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$a=\frac{-42±\sqrt{1764-36\left(-49\right)}}{2\times 9}$$

Whakareatia -36 ki te -49.

$$a=\frac{-42±\sqrt{1764+1764}}{2\times 9}$$

Tāpiri 1764 ki te 1764.

$$a=\frac{-42±\sqrt{3528}}{2\times 9}$$

Tuhia te pūtakerua o te 3528.

$$a=\frac{-42±42\sqrt{2}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$a=\frac{-42±42\sqrt{2}}{18}$$

Nā, me whakaoti te whārite a=\frac{-42±42\sqrt{2}}{18} ina he tāpiri te ±. Tāpiri -42 ki te 42\sqrt{2}.

$$a=\frac{42\sqrt{2}-42}{18}$$

Whakawehe -42+42\sqrt{2} ki te 18.

$$a=\frac{7\sqrt{2}-7}{3}$$

Nā, me whakaoti te whārite a=\frac{-42±42\sqrt{2}}{18} ina he tango te ±. Tango 42\sqrt{2} mai i -42.

$$a=\frac{-42\sqrt{2}-42}{18}$$

Whakawehe -42-42\sqrt{2} ki te 18.

$$a=\frac{-7\sqrt{2}-7}{3}$$

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 \frac{-7+7\sqrt{2}}{3} mō te x_{1} me te \frac{-7-7\sqrt{2}}{3} mō te x_{2}.

$$9a^{2}+42a-49=9\left(a-\frac{7\sqrt{2}-7}{3}\right)\left(a-\frac{-7\sqrt{2}-7}{3}\right)$$

Aromātai

$$9a^{2}+42a-49$$