Whakaoti i te -20x^2+66x-20

$$-20 { x }^{ 2 } +66x-20$$

Tauwehe

$$-20\left(x-\frac{33-\sqrt{689}}{20}\right)\left(x-\frac{\sqrt{689}+33}{20}\right)$$

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.

$$-20x^{2}+66x-20=0$$

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.

$$x=\frac{-66±\sqrt{66^{2}-4\left(-20\right)\left(-20\right)}}{2\left(-20\right)}$$

Pūrua 66.

$$x=\frac{-66±\sqrt{4356-4\left(-20\right)\left(-20\right)}}{2\left(-20\right)}$$

Whakareatia -4 ki te -20.

$$x=\frac{-66±\sqrt{4356+80\left(-20\right)}}{2\left(-20\right)}$$

Whakareatia 80 ki te -20.

$$x=\frac{-66±\sqrt{4356-1600}}{2\left(-20\right)}$$

Tāpiri 4356 ki te -1600.

$$x=\frac{-66±\sqrt{2756}}{2\left(-20\right)}$$

Tuhia te pūtakerua o te 2756.

$$x=\frac{-66±2\sqrt{689}}{2\left(-20\right)}$$

Whakareatia 2 ki te -20.

$$x=\frac{-66±2\sqrt{689}}{-40}$$

Nā, me whakaoti te whārite x=\frac{-66±2\sqrt{689}}{-40} ina he tāpiri te ±. Tāpiri -66 ki te 2\sqrt{689}.

$$x=\frac{2\sqrt{689}-66}{-40}$$

Whakawehe -66+2\sqrt{689} ki te -40.

$$x=\frac{33-\sqrt{689}}{20}$$

Nā, me whakaoti te whārite x=\frac{-66±2\sqrt{689}}{-40} ina he tango te ±. Tango 2\sqrt{689} mai i -66.

$$x=\frac{-2\sqrt{689}-66}{-40}$$

Whakawehe -66-2\sqrt{689} ki te -40.

$$x=\frac{\sqrt{689}+33}{20}$$

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{33-\sqrt{689}}{20} mō te x_{1} me te \frac{33+\sqrt{689}}{20} mō te x_{2}.

$$-20x^{2}+66x-20=-20\left(x-\frac{33-\sqrt{689}}{20}\right)\left(x-\frac{\sqrt{689}+33}{20}\right)$$

Aromātai

$$-20x^{2}+66x-20$$