Whakaoti i te x^2-20x-192=0

$$x ^ { 2 } - 20 x - 192 = 0$$

Whakaoti mō x

$$x=2\sqrt{73}+10\approx 27.088007491$$

$$x=10-2\sqrt{73}\approx -7.088007491$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$x^{2}-20x-192=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -20 mō b, me -192 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\left(-192\right)}}{2}$$

Pūrua -20.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\left(-192\right)}}{2}$$

Whakareatia -4 ki te -192.

$$x=\frac{-\left(-20\right)±\sqrt{400+768}}{2}$$

Tāpiri 400 ki te 768.

$$x=\frac{-\left(-20\right)±\sqrt{1168}}{2}$$

Tuhia te pūtakerua o te 1168.

$$x=\frac{-\left(-20\right)±4\sqrt{73}}{2}$$

Ko te tauaro o -20 ko 20.

$$x=\frac{20±4\sqrt{73}}{2}$$

Nā, me whakaoti te whārite x=\frac{20±4\sqrt{73}}{2} ina he tāpiri te ±. Tāpiri 20 ki te 4\sqrt{73}.

$$x=\frac{4\sqrt{73}+20}{2}$$

Whakawehe 20+4\sqrt{73} ki te 2.

$$x=2\sqrt{73}+10$$

Nā, me whakaoti te whārite x=\frac{20±4\sqrt{73}}{2} ina he tango te ±. Tango 4\sqrt{73} mai i 20.

$$x=\frac{20-4\sqrt{73}}{2}$$

Whakawehe 20-4\sqrt{73} ki te 2.

$$x=10-2\sqrt{73}$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{73}+10 x=10-2\sqrt{73}$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$x^{2}-20x-192=0$$

Me tāpiri 192 ki ngā taha e rua o te whārite.

$$x^{2}-20x-192-\left(-192\right)=-\left(-192\right)$$

Mā te tango i te -192 i a ia ake anō ka toe ko te 0.

$$x^{2}-20x=-\left(-192\right)$$

Tango -192 mai i 0.

$$x^{2}-20x=192$$

Whakawehea te -20, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -10. Nā, tāpiria te pūrua o te -10 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-20x+\left(-10\right)^{2}=192+\left(-10\right)^{2}$$

Pūrua -10.

$$x^{2}-20x+100=192+100$$

Tāpiri 192 ki te 100.

$$x^{2}-20x+100=292$$

Tauwehea x^{2}-20x+100. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-10\right)^{2}=292$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x-10\right)^{2}}=\sqrt{292}$$

Whakarūnātia.

$$x-10=2\sqrt{73} x-10=-2\sqrt{73}$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$x=2\sqrt{73}+10 x=10-2\sqrt{73}$$