Whakaoti i te 5x^2-3x=

$$5 x ^ { 2 } - 3 x =$$

Tauwehe

$$x\left(5x-3\right)$$

Ngā Upane Otinga

Tauwehea te x.

$$x\left(5x-3\right)$$

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.

$$5x^{2}-3x=0$$

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.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\times 5}$$

Tuhia te pūtakerua o te \left(-3\right)^{2}.

$$x=\frac{-\left(-3\right)±3}{2\times 5}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±3}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{3±3}{10}$$

Nā, me whakaoti te whārite x=\frac{3±3}{10} ina he tāpiri te ±. Tāpiri 3 ki te 3.

$$x=\frac{6}{10}$$

Whakahekea te hautanga \frac{6}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{3}{5}$$

Nā, me whakaoti te whārite x=\frac{3±3}{10} ina he tango te ±. Tango 3 mai i 3.

$$x=\frac{0}{10}$$

Whakawehe 0 ki te 10.

$$x=0$$

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{3}{5} mō te x_{1} me te 0 mō te x_{2}.

$$5x^{2}-3x=5\left(x-\frac{3}{5}\right)x$$

Tango \frac{3}{5} mai i x mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$5x^{2}-3x=5\times \frac{5x-3}{5}x$$

Whakakorea atu te tauwehe pūnoa nui rawa 5 i roto i te 5 me te 5.

$$5x^{2}-3x=\left(5x-3\right)x$$

Aromātai

$$x\left(5x-3\right)$$