Whakaoti i te 15c-9c^2

$$15c-9 { c }^{ 2 }$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 3.

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

Whakaarohia te 5c-3c^{2}. Tauwehea te c.

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$3c\left(-3c+5\right)$$

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.

$$-9c^{2}+15c=0$$

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.

$$c=\frac{-15±\sqrt{15^{2}}}{2\left(-9\right)}$$

Tuhia te pūtakerua o te 15^{2}.

$$c=\frac{-15±15}{2\left(-9\right)}$$

Whakareatia 2 ki te -9.

$$c=\frac{-15±15}{-18}$$

Nā, me whakaoti te whārite c=\frac{-15±15}{-18} ina he tāpiri te ±. Tāpiri -15 ki te 15.

$$c=\frac{0}{-18}$$

Whakawehe 0 ki te -18.

$$c=0$$

Nā, me whakaoti te whārite c=\frac{-15±15}{-18} ina he tango te ±. Tango 15 mai i -15.

$$c=-\frac{30}{-18}$$

Whakahekea te hautanga \frac{-30}{-18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

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

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

$$-9c^{2}+15c=-9c\left(c-\frac{5}{3}\right)$$

Tango \frac{5}{3} mai i c 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.

$$-9c^{2}+15c=-9c\times \frac{-3c+5}{-3}$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te -9 me te -3.

$$-9c^{2}+15c=3c\left(-3c+5\right)$$

Aromātai

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