Whakaoti i te 4t^2+16t+9

$$4 t ^ { 2 } + 16 t + 9$$

Tauwehe

$$4\left(t-\left(-\frac{\sqrt{7}}{2}-2\right)\right)\left(t-\left(\frac{\sqrt{7}}{2}-2\right)\right)$$

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.

$$4t^{2}+16t+9=0$$

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.

$$t=\frac{-16±\sqrt{16^{2}-4\times 4\times 9}}{2\times 4}$$

Pūrua 16.

$$t=\frac{-16±\sqrt{256-4\times 4\times 9}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$t=\frac{-16±\sqrt{256-16\times 9}}{2\times 4}$$

Whakareatia -16 ki te 9.

$$t=\frac{-16±\sqrt{256-144}}{2\times 4}$$

Tāpiri 256 ki te -144.

$$t=\frac{-16±\sqrt{112}}{2\times 4}$$

Tuhia te pūtakerua o te 112.

$$t=\frac{-16±4\sqrt{7}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$t=\frac{-16±4\sqrt{7}}{8}$$

Nā, me whakaoti te whārite t=\frac{-16±4\sqrt{7}}{8} ina he tāpiri te ±. Tāpiri -16 ki te 4\sqrt{7}.

$$t=\frac{4\sqrt{7}-16}{8}$$

Whakawehe -16+4\sqrt{7} ki te 8.

$$t=\frac{\sqrt{7}}{2}-2$$

Nā, me whakaoti te whārite t=\frac{-16±4\sqrt{7}}{8} ina he tango te ±. Tango 4\sqrt{7} mai i -16.

$$t=\frac{-4\sqrt{7}-16}{8}$$

Whakawehe -16-4\sqrt{7} ki te 8.

$$t=-\frac{\sqrt{7}}{2}-2$$

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 -2+\frac{\sqrt{7}}{2} mō te x_{1} me te -2-\frac{\sqrt{7}}{2} mō te x_{2}.

$$4t^{2}+16t+9=4\left(t-\left(\frac{\sqrt{7}}{2}-2\right)\right)\left(t-\left(-\frac{\sqrt{7}}{2}-2\right)\right)$$

Aromātai

$$4t^{2}+16t+9$$