Whakaoti i te 5x^2-125=0

$$5 { x }^{ 2 } -125=0$$

Whakaoti mō x

$$x=5$$

$$x=-5$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 5.

$$x^{2}-25=0$$

Whakaarohia te x^{2}-25. Tuhia anō te x^{2}-25 hei x^{2}-5^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-5\right)\left(x+5\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-5=0 me te x+5=0.

$$x=5 x=-5$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 125 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$5x^{2}=125$$

Whakawehea ngā taha e rua ki te 5.

$$x^{2}=\frac{125}{5}$$

Whakawehea te 125 ki te 5, kia riro ko 25.

$$x^{2}=25$$

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

$$x=5 x=-5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$5x^{2}-125=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me -125 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-125\right)}}{2\times 5}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-125\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{0±\sqrt{-20\left(-125\right)}}{2\times 5}$$

Whakareatia -20 ki te -125.

$$x=\frac{0±\sqrt{2500}}{2\times 5}$$

Tuhia te pūtakerua o te 2500.

$$x=\frac{0±50}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{0±50}{10}$$

Nā, me whakaoti te whārite x=\frac{0±50}{10} ina he tāpiri te ±. Whakawehe 50 ki te 10.

$$x=5$$

Nā, me whakaoti te whārite x=\frac{0±50}{10} ina he tango te ±. Whakawehe -50 ki te 10.

$$x=-5$$

Kua oti te whārite te whakatau.

$$x=5 x=-5$$