Whakaoti i te 5x^2-1-7=0

$$5 x ^ { 2 } - 1 - 7 = 0$$

Whakaoti mō x

$$x = \frac{2 \sqrt{10}}{5} \approx 1.264911064$$

$$x = -\frac{2 \sqrt{10}}{5} \approx -1.264911064$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 7 i te -1, ka -8.

$$5x^{2}-8=0$$

Me tāpiri te 8 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$5x^{2}=8$$

Whakawehea ngā taha e rua ki te 5.

$$x^{2}=\frac{8}{5}$$

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

$$x=\frac{2\sqrt{10}}{5} x=-\frac{2\sqrt{10}}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 7 i te -1, ka -8.

$$5x^{2}-8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-8\right)}}{2\times 5}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-8\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{0±\sqrt{-20\left(-8\right)}}{2\times 5}$$

Whakareatia -20 ki te -8.

$$x=\frac{0±\sqrt{160}}{2\times 5}$$

Tuhia te pūtakerua o te 160.

$$x=\frac{0±4\sqrt{10}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{0±4\sqrt{10}}{10}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{10}}{10} ina he tāpiri te ±.

$$x=\frac{2\sqrt{10}}{5}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{10}}{10} ina he tango te ±.

$$x=-\frac{2\sqrt{10}}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{10}}{5} x=-\frac{2\sqrt{10}}{5}$$