Whakaoti i te 1/2x^2-32=0

$$\frac { 1 } { 2 } x ^ { 2 } - 32 = 0$$

Whakaoti mō x

$$x=8$$

$$x=-8$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Me whakarea ngā taha e rua ki te 2.

$$x^{2}-64=0$$

Whakaarohia te x^{2}-64. Tuhia anō te x^{2}-64 hei x^{2}-8^{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).

$$\left(x-8\right)\left(x+8\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-8=0 me te x+8=0.

$$x=8 x=-8$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 32 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$\frac{1}{2}x^{2}=32$$

Me whakarea ngā taha e rua ki te 2, te tau utu o \frac{1}{2}.

$$x^{2}=32\times 2$$

Whakareatia te 32 ki te 2, ka 64.

$$x^{2}=64$$

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

$$x=8 x=-8$$

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.

$$\frac{1}{2}x^{2}-32=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{1}{2} mō a, 0 mō b, me -32 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}\left(-32\right)}}{2\times \frac{1}{2}}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{2}\left(-32\right)}}{2\times \frac{1}{2}}$$

Whakareatia -4 ki te \frac{1}{2}.

$$x=\frac{0±\sqrt{-2\left(-32\right)}}{2\times \frac{1}{2}}$$

Whakareatia -2 ki te -32.

$$x=\frac{0±\sqrt{64}}{2\times \frac{1}{2}}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{0±8}{2\times \frac{1}{2}}$$

Whakareatia 2 ki te \frac{1}{2}.

$$x=\frac{0±8}{1}$$

Nā, me whakaoti te whārite x=\frac{0±8}{1} ina he tāpiri te ±.

$$x=8$$

Nā, me whakaoti te whārite x=\frac{0±8}{1} ina he tango te ±.

$$x=-8$$

Kua oti te whārite te whakatau.

$$x=8 x=-8$$