Whakaoti i te x^1-16x^2+28

$$x ^ { 1 } - 16 x ^ { 2 } + 28$$

Tauwehe

$$-16\left(x-\frac{1-\sqrt{1793}}{32}\right)\left(x-\frac{\sqrt{1793}+1}{32}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te x mā te pū o 1, kia riro ko x.

$$factor(x-16x^{2}+28)$$

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.

$$-16x^{2}+x+28=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-16\right)\times 28}}{2\left(-16\right)}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\left(-16\right)\times 28}}{2\left(-16\right)}$$

Whakareatia -4 ki te -16.

$$x=\frac{-1±\sqrt{1+64\times 28}}{2\left(-16\right)}$$

Whakareatia 64 ki te 28.

$$x=\frac{-1±\sqrt{1+1792}}{2\left(-16\right)}$$

Tāpiri 1 ki te 1792.

$$x=\frac{-1±\sqrt{1793}}{2\left(-16\right)}$$

Whakareatia 2 ki te -16.

$$x=\frac{-1±\sqrt{1793}}{-32}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{1793}}{-32} ina he tāpiri te ±. Tāpiri -1 ki te \sqrt{1793}.

$$x=\frac{\sqrt{1793}-1}{-32}$$

Whakawehe -1+\sqrt{1793} ki te -32.

$$x=\frac{1-\sqrt{1793}}{32}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{1793}}{-32} ina he tango te ±. Tango \sqrt{1793} mai i -1.

$$x=\frac{-\sqrt{1793}-1}{-32}$$

Whakawehe -1-\sqrt{1793} ki te -32.

$$x=\frac{\sqrt{1793}+1}{32}$$

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{1793}}{32} mō te x_{1} me te \frac{1+\sqrt{1793}}{32} mō te x_{2}.

$$-16x^{2}+x+28=-16\left(x-\frac{1-\sqrt{1793}}{32}\right)\left(x-\frac{\sqrt{1793}+1}{32}\right)$$

Aromātai

$$28+x-16x^{2}$$

Ngā Upane Otinga

Tātaihia te x mā te pū o 1, kia riro ko x.

$$x-16x^{2}+28$$