Whakaoti i te 36x^2+8x-16=

$$36 x ^ { 2 } + 8 x - 16 =$$

Tauwehe

$$36\left(x-\frac{-\sqrt{37}-1}{9}\right)\left(x-\frac{\sqrt{37}-1}{9}\right)$$

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.

$$36x^{2}+8x-16=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\times 36\left(-16\right)}}{2\times 36}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 36\left(-16\right)}}{2\times 36}$$

Whakareatia -4 ki te 36.

$$x=\frac{-8±\sqrt{64-144\left(-16\right)}}{2\times 36}$$

Whakareatia -144 ki te -16.

$$x=\frac{-8±\sqrt{64+2304}}{2\times 36}$$

Tāpiri 64 ki te 2304.

$$x=\frac{-8±\sqrt{2368}}{2\times 36}$$

Tuhia te pūtakerua o te 2368.

$$x=\frac{-8±8\sqrt{37}}{2\times 36}$$

Whakareatia 2 ki te 36.

$$x=\frac{-8±8\sqrt{37}}{72}$$

Nā, me whakaoti te whārite x=\frac{-8±8\sqrt{37}}{72} ina he tāpiri te ±. Tāpiri -8 ki te 8\sqrt{37}.

$$x=\frac{8\sqrt{37}-8}{72}$$

Whakawehe -8+8\sqrt{37} ki te 72.

$$x=\frac{\sqrt{37}-1}{9}$$

Nā, me whakaoti te whārite x=\frac{-8±8\sqrt{37}}{72} ina he tango te ±. Tango 8\sqrt{37} mai i -8.

$$x=\frac{-8\sqrt{37}-8}{72}$$

Whakawehe -8-8\sqrt{37} ki te 72.

$$x=\frac{-\sqrt{37}-1}{9}$$

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{-1+\sqrt{37}}{9} mō te x_{1} me te \frac{-1-\sqrt{37}}{9} mō te x_{2}.

$$36x^{2}+8x-16=36\left(x-\frac{\sqrt{37}-1}{9}\right)\left(x-\frac{-\sqrt{37}-1}{9}\right)$$

Aromātai

$$36x^{2}+8x-16$$