Whakaoti i te 6x^2+20x-420

$$6 { x }^{ 2 } +20x-420$$

Tauwehe

$$6\left(x-\frac{-\sqrt{655}-5}{3}\right)\left(x-\frac{\sqrt{655}-5}{3}\right)$$

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.

$$6x^{2}+20x-420=0$$

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.

$$x=\frac{-20±\sqrt{20^{2}-4\times 6\left(-420\right)}}{2\times 6}$$

Pūrua 20.

$$x=\frac{-20±\sqrt{400-4\times 6\left(-420\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-20±\sqrt{400-24\left(-420\right)}}{2\times 6}$$

Whakareatia -24 ki te -420.

$$x=\frac{-20±\sqrt{400+10080}}{2\times 6}$$

Tāpiri 400 ki te 10080.

$$x=\frac{-20±\sqrt{10480}}{2\times 6}$$

Tuhia te pūtakerua o te 10480.

$$x=\frac{-20±4\sqrt{655}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-20±4\sqrt{655}}{12}$$

Nā, me whakaoti te whārite x=\frac{-20±4\sqrt{655}}{12} ina he tāpiri te ±. Tāpiri -20 ki te 4\sqrt{655}.

$$x=\frac{4\sqrt{655}-20}{12}$$

Whakawehe -20+4\sqrt{655} ki te 12.

$$x=\frac{\sqrt{655}-5}{3}$$

Nā, me whakaoti te whārite x=\frac{-20±4\sqrt{655}}{12} ina he tango te ±. Tango 4\sqrt{655} mai i -20.

$$x=\frac{-4\sqrt{655}-20}{12}$$

Whakawehe -20-4\sqrt{655} ki te 12.

$$x=\frac{-\sqrt{655}-5}{3}$$

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{-5+\sqrt{655}}{3} mō te x_{1} me te \frac{-5-\sqrt{655}}{3} mō te x_{2}.

$$6x^{2}+20x-420=6\left(x-\frac{\sqrt{655}-5}{3}\right)\left(x-\frac{-\sqrt{655}-5}{3}\right)$$

Aromātai

$$6x^{2}+20x-420$$