Whakaoti i te 35x^2+38x-41

$$35 x ^ { 2 } + 38 x - 41$$

Tauwehe

$$35\left(x-\frac{-2\sqrt{449}-19}{35}\right)\left(x-\frac{2\sqrt{449}-19}{35}\right)$$

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.

$$35x^{2}+38x-41=0$$

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.

$$x=\frac{-38±\sqrt{38^{2}-4\times 35\left(-41\right)}}{2\times 35}$$

Pūrua 38.

$$x=\frac{-38±\sqrt{1444-4\times 35\left(-41\right)}}{2\times 35}$$

Whakareatia -4 ki te 35.

$$x=\frac{-38±\sqrt{1444-140\left(-41\right)}}{2\times 35}$$

Whakareatia -140 ki te -41.

$$x=\frac{-38±\sqrt{1444+5740}}{2\times 35}$$

Tāpiri 1444 ki te 5740.

$$x=\frac{-38±\sqrt{7184}}{2\times 35}$$

Tuhia te pūtakerua o te 7184.

$$x=\frac{-38±4\sqrt{449}}{2\times 35}$$

Whakareatia 2 ki te 35.

$$x=\frac{-38±4\sqrt{449}}{70}$$

Nā, me whakaoti te whārite x=\frac{-38±4\sqrt{449}}{70} ina he tāpiri te ±. Tāpiri -38 ki te 4\sqrt{449}.

$$x=\frac{4\sqrt{449}-38}{70}$$

Whakawehe -38+4\sqrt{449} ki te 70.

$$x=\frac{2\sqrt{449}-19}{35}$$

Nā, me whakaoti te whārite x=\frac{-38±4\sqrt{449}}{70} ina he tango te ±. Tango 4\sqrt{449} mai i -38.

$$x=\frac{-4\sqrt{449}-38}{70}$$

Whakawehe -38-4\sqrt{449} ki te 70.

$$x=\frac{-2\sqrt{449}-19}{35}$$

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{-19+2\sqrt{449}}{35} mō te x_{1} me te \frac{-19-2\sqrt{449}}{35} mō te x_{2}.

$$35x^{2}+38x-41=35\left(x-\frac{2\sqrt{449}-19}{35}\right)\left(x-\frac{-2\sqrt{449}-19}{35}\right)$$

Aromātai

$$35x^{2}+38x-41$$