Whakaoti i te 5x^2-45=03a

$$5 x ^ { 2 } - 45 = 03 a$$

Whakaoti mō x

$$x=3$$

$$x=-3$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakareatia te 0 ki te 3, ka 0.

$$5x^{2}-45=0a$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$5x^{2}-45=0$$

Whakawehea ngā taha e rua ki te 5.

$$x^{2}-9=0$$

Whakaarohia te x^{2}-9. Tuhia anō te x^{2}-9 hei x^{2}-3^{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).

$$\left(x-3\right)\left(x+3\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-3=0 me te x+3=0.

$$x=3 x=-3$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te 0 ki te 3, ka 0.

$$5x^{2}-45=0a$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$5x^{2}-45=0$$

Me tāpiri te 45 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$5x^{2}=45$$

Whakawehea ngā taha e rua ki te 5.

$$x^{2}=\frac{45}{5}$$

Whakawehea te 45 ki te 5, kia riro ko 9.

$$x^{2}=9$$

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

$$x=3 x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 3, ka 0.

$$5x^{2}-45=0a$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$5x^{2}-45=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me -45 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-45\right)}}{2\times 5}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-45\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{0±\sqrt{-20\left(-45\right)}}{2\times 5}$$

Whakareatia -20 ki te -45.

$$x=\frac{0±\sqrt{900}}{2\times 5}$$

Tuhia te pūtakerua o te 900.

$$x=\frac{0±30}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{0±30}{10}$$

Nā, me whakaoti te whārite x=\frac{0±30}{10} ina he tāpiri te ±. Whakawehe 30 ki te 10.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{0±30}{10} ina he tango te ±. Whakawehe -30 ki te 10.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=3 x=-3$$

Whakaoti mō a (complex solution)

$$a\in \mathrm{C}$$

$$x=3\text{ or }x=-3$$

Whakaoti mō a

$$a\in \mathrm{R}$$

$$|x|=3$$