Whakaoti i te g(x)=-2x^2+3x

$$g ( x ) = - 2 x ^ { 2 } + 3 x$$

Tauwehe

$$x\left(3-2x\right)$$

Ngā Upane Otinga

Tauwehea te x.

$$x\left(-2x+3\right)$$

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.

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

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.

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

Tuhia te pūtakerua o te 3^{2}.

$$x=\frac{-3±3}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-3±3}{-4}$$

Nā, me whakaoti te whārite x=\frac{-3±3}{-4} ina he tāpiri te ±. Tāpiri -3 ki te 3.

$$x=\frac{0}{-4}$$

Whakawehe 0 ki te -4.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-3±3}{-4} ina he tango te ±. Tango 3 mai i -3.

$$x=-\frac{6}{-4}$$

Whakahekea te hautanga \frac{-6}{-4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{3}{2}$$

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{3}{2} mō te x_{2}.

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

Tango \frac{3}{2} 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.

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

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

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

Aromātai

$$x\left(3-2x\right)$$