Whakaoti i te 10c^2+25c

$$10 c ^ { 2 } + 25 c$$

Tauwehe

$$5c\left(2c+5\right)$$

Ngā Upane Otinga

Tauwehea te 5.

$$5\left(2c^{2}+5c\right)$$

Whakaarohia te 2c^{2}+5c. Tauwehea te c.

$$c\left(2c+5\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$5c\left(2c+5\right)$$

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.

$$10c^{2}+25c=0$$

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.

$$c=\frac{-25±\sqrt{25^{2}}}{2\times 10}$$

Tuhia te pūtakerua o te 25^{2}.

$$c=\frac{-25±25}{2\times 10}$$

Whakareatia 2 ki te 10.

$$c=\frac{-25±25}{20}$$

Nā, me whakaoti te whārite c=\frac{-25±25}{20} ina he tāpiri te ±. Tāpiri -25 ki te 25.

$$c=\frac{0}{20}$$

Whakawehe 0 ki te 20.

$$c=0$$

Nā, me whakaoti te whārite c=\frac{-25±25}{20} ina he tango te ±. Tango 25 mai i -25.

$$c=-\frac{50}{20}$$

Whakahekea te hautanga \frac{-50}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$c=-\frac{5}{2}$$

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 0 mō te x_{1} me te -\frac{5}{2} mō te x_{2}.

$$10c^{2}+25c=10c\left(c-\left(-\frac{5}{2}\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$10c^{2}+25c=10c\left(c+\frac{5}{2}\right)$$

Tāpiri \frac{5}{2} ki te c mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$10c^{2}+25c=10c\times \frac{2c+5}{2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 10 me te 2.

$$10c^{2}+25c=5c\left(2c+5\right)$$

Aromātai

$$5c\left(2c+5\right)$$