Whakaoti i te =4x-10+16-49x^2

$$= 4 x - 10 + 16 - 49 x ^ { 2 }$$

Tauwehe

$$-49\left(x-\frac{2-\sqrt{298}}{49}\right)\left(x-\frac{\sqrt{298}+2}{49}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te -10 ki te 16, ka 6.

$$factor(4x+6-49x^{2})$$

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.

$$-49x^{2}+4x+6=0$$

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.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-49\right)\times 6}}{2\left(-49\right)}$$

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\left(-49\right)\times 6}}{2\left(-49\right)}$$

Whakareatia -4 ki te -49.

$$x=\frac{-4±\sqrt{16+196\times 6}}{2\left(-49\right)}$$

Whakareatia 196 ki te 6.

$$x=\frac{-4±\sqrt{16+1176}}{2\left(-49\right)}$$

Tāpiri 16 ki te 1176.

$$x=\frac{-4±\sqrt{1192}}{2\left(-49\right)}$$

Tuhia te pūtakerua o te 1192.

$$x=\frac{-4±2\sqrt{298}}{2\left(-49\right)}$$

Whakareatia 2 ki te -49.

$$x=\frac{-4±2\sqrt{298}}{-98}$$

Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{298}}{-98} ina he tāpiri te ±. Tāpiri -4 ki te 2\sqrt{298}.

$$x=\frac{2\sqrt{298}-4}{-98}$$

Whakawehe -4+2\sqrt{298} ki te -98.

$$x=\frac{2-\sqrt{298}}{49}$$

Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{298}}{-98} ina he tango te ±. Tango 2\sqrt{298} mai i -4.

$$x=\frac{-2\sqrt{298}-4}{-98}$$

Whakawehe -4-2\sqrt{298} ki te -98.

$$x=\frac{\sqrt{298}+2}{49}$$

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{2-\sqrt{298}}{49} mō te x_{1} me te \frac{2+\sqrt{298}}{49} mō te x_{2}.

$$-49x^{2}+4x+6=-49\left(x-\frac{2-\sqrt{298}}{49}\right)\left(x-\frac{\sqrt{298}+2}{49}\right)$$

Aromātai

$$6+4x-49x^{2}$$

Ngā Upane Otinga

Tāpirihia te -10 ki te 16, ka 6.

$$4x+6-49x^{2}$$