Whakaoti i te 3x^2-50x-26

$$3 { x }^{ 2 } -50x-26$$

Tauwehe

$$3\left(x-\frac{25-\sqrt{703}}{3}\right)\left(x-\frac{\sqrt{703}+25}{3}\right)$$

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.

$$3x^{2}-50x-26=0$$

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.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}-4\times 3\left(-26\right)}}{2\times 3}$$

Pūrua -50.

$$x=\frac{-\left(-50\right)±\sqrt{2500-4\times 3\left(-26\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-50\right)±\sqrt{2500-12\left(-26\right)}}{2\times 3}$$

Whakareatia -12 ki te -26.

$$x=\frac{-\left(-50\right)±\sqrt{2500+312}}{2\times 3}$$

Tāpiri 2500 ki te 312.

$$x=\frac{-\left(-50\right)±\sqrt{2812}}{2\times 3}$$

Tuhia te pūtakerua o te 2812.

$$x=\frac{-\left(-50\right)±2\sqrt{703}}{2\times 3}$$

Ko te tauaro o -50 ko 50.

$$x=\frac{50±2\sqrt{703}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{50±2\sqrt{703}}{6}$$

Nā, me whakaoti te whārite x=\frac{50±2\sqrt{703}}{6} ina he tāpiri te ±. Tāpiri 50 ki te 2\sqrt{703}.

$$x=\frac{2\sqrt{703}+50}{6}$$

Whakawehe 50+2\sqrt{703} ki te 6.

$$x=\frac{\sqrt{703}+25}{3}$$

Nā, me whakaoti te whārite x=\frac{50±2\sqrt{703}}{6} ina he tango te ±. Tango 2\sqrt{703} mai i 50.

$$x=\frac{50-2\sqrt{703}}{6}$$

Whakawehe 50-2\sqrt{703} ki te 6.

$$x=\frac{25-\sqrt{703}}{3}$$

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{25+\sqrt{703}}{3} mō te x_{1} me te \frac{25-\sqrt{703}}{3} mō te x_{2}.

$$3x^{2}-50x-26=3\left(x-\frac{\sqrt{703}+25}{3}\right)\left(x-\frac{25-\sqrt{703}}{3}\right)$$

Aromātai

$$3x^{2}-50x-26$$