Whakaoti i te 5x^2-4=1900

$$5 x ^ { 2 } - 4 = 1900$$

Whakaoti mō x

$$x = \frac{4 \sqrt{595}}{5} \approx 19.514097468$$

$$x = -\frac{4 \sqrt{595}}{5} \approx -19.514097468$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 4 ki ngā taha e rua.

$$5x^{2}=1900+4$$

Tāpirihia te 1900 ki te 4, ka 1904.

$$5x^{2}=1904$$

Whakawehea ngā taha e rua ki te 5.

$$x^{2}=\frac{1904}{5}$$

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

$$x=\frac{4\sqrt{595}}{5} x=-\frac{4\sqrt{595}}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 1900 mai i ngā taha e rua.

$$5x^{2}-4-1900=0$$

Tangohia te 1900 i te -4, ka -1904.

$$5x^{2}-1904=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me -1904 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-1904\right)}}{2\times 5}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-1904\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{0±\sqrt{-20\left(-1904\right)}}{2\times 5}$$

Whakareatia -20 ki te -1904.

$$x=\frac{0±\sqrt{38080}}{2\times 5}$$

Tuhia te pūtakerua o te 38080.

$$x=\frac{0±8\sqrt{595}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{0±8\sqrt{595}}{10}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{595}}{10} ina he tāpiri te ±.

$$x=\frac{4\sqrt{595}}{5}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{595}}{10} ina he tango te ±.

$$x=-\frac{4\sqrt{595}}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{4\sqrt{595}}{5} x=-\frac{4\sqrt{595}}{5}$$