Whakaoti i te -4x^2+1=0

$$-4 { x }^{ 2 } +1=0$$

Whakaoti mō x

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 1 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-4x^{2}=-1$$

Whakawehea ngā taha e rua ki te -4.

$$x^{2}=\frac{-1}{-4}$$

Ka taea te hautanga \frac{-1}{-4} te whakamāmā ki te \frac{1}{4} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x^{2}=\frac{1}{4}$$

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

$$x=\frac{1}{2} x=-\frac{1}{2}$$

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.

$$-4x^{2}+1=0$$

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

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

Pūrua 0.

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

Whakareatia -4 ki te -4.

$$x=\frac{0±\sqrt{16}}{2\left(-4\right)}$$

Tuhia te pūtakerua o te 16.

$$x=\frac{0±4}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{0±4}{-8}$$

Nā, me whakaoti te whārite x=\frac{0±4}{-8} ina he tāpiri te ±. Whakahekea te hautanga \frac{4}{-8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=-\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{0±4}{-8} ina he tango te ±. Whakahekea te hautanga \frac{-4}{-8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Kua oti te whārite te whakatau.

$$x=-\frac{1}{2} x=\frac{1}{2}$$