Whakaoti i te 5x^2-40x-4=

$$5 x ^ { 2 } - 40 x - 4 =$$

Tauwehe

$$5\left(x-\left(-\frac{2\sqrt{105}}{5}+4\right)\right)\left(x-\left(\frac{2\sqrt{105}}{5}+4\right)\right)$$

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.

$$5x^{2}-40x-4=0$$

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.

$$x=\frac{-\left(-40\right)±\sqrt{\left(-40\right)^{2}-4\times 5\left(-4\right)}}{2\times 5}$$

Pūrua -40.

$$x=\frac{-\left(-40\right)±\sqrt{1600-4\times 5\left(-4\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-40\right)±\sqrt{1600-20\left(-4\right)}}{2\times 5}$$

Whakareatia -20 ki te -4.

$$x=\frac{-\left(-40\right)±\sqrt{1600+80}}{2\times 5}$$

Tāpiri 1600 ki te 80.

$$x=\frac{-\left(-40\right)±\sqrt{1680}}{2\times 5}$$

Tuhia te pūtakerua o te 1680.

$$x=\frac{-\left(-40\right)±4\sqrt{105}}{2\times 5}$$

Ko te tauaro o -40 ko 40.

$$x=\frac{40±4\sqrt{105}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{40±4\sqrt{105}}{10}$$

Nā, me whakaoti te whārite x=\frac{40±4\sqrt{105}}{10} ina he tāpiri te ±. Tāpiri 40 ki te 4\sqrt{105}.

$$x=\frac{4\sqrt{105}+40}{10}$$

Whakawehe 40+4\sqrt{105} ki te 10.

$$x=\frac{2\sqrt{105}}{5}+4$$

Nā, me whakaoti te whārite x=\frac{40±4\sqrt{105}}{10} ina he tango te ±. Tango 4\sqrt{105} mai i 40.

$$x=\frac{40-4\sqrt{105}}{10}$$

Whakawehe 40-4\sqrt{105} ki te 10.

$$x=-\frac{2\sqrt{105}}{5}+4$$

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 4+\frac{2\sqrt{105}}{5} mō te x_{1} me te 4-\frac{2\sqrt{105}}{5} mō te x_{2}.

$$5x^{2}-40x-4=5\left(x-\left(\frac{2\sqrt{105}}{5}+4\right)\right)\left(x-\left(-\frac{2\sqrt{105}}{5}+4\right)\right)$$

Aromātai

$$5x^{2}-40x-4$$