Whakaoti i te 4x^2-25=0

$$4 x ^ { 2 } - 25 = 0$$

Whakaoti mō x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakaarohia te 4x^{2}-25. Tuhia anō te 4x^{2}-25 hei \left(2x\right)^{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).

$$\left(2x-5\right)\left(2x+5\right)=0$$

Hei kimi otinga whārite, me whakaoti te 2x-5=0 me te 2x+5=0.

$$x=\frac{5}{2} x=-\frac{5}{2}$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 25 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$4x^{2}=25$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{25}{4}$$

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

$$x=\frac{5}{2} x=-\frac{5}{2}$$

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.

$$4x^{2}-25=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 0 mō b, me -25 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-25\right)}}{2\times 4}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-25\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\left(-25\right)}}{2\times 4}$$

Whakareatia -16 ki te -25.

$$x=\frac{0±\sqrt{400}}{2\times 4}$$

Tuhia te pūtakerua o te 400.

$$x=\frac{0±20}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±20}{8}$$

Nā, me whakaoti te whārite x=\frac{0±20}{8} ina he tāpiri te ±. Whakahekea te hautanga \frac{20}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Nā, me whakaoti te whārite x=\frac{0±20}{8} ina he tango te ±. Whakahekea te hautanga \frac{-20}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=-\frac{5}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{5}{2} x=-\frac{5}{2}$$