Whakaoti i te 2x^2-10=30

$$2 x ^ { 2 } - 10 = 30$$

Whakaoti mō x

$$x=2\sqrt{5}\approx 4.472135955$$

$$x=-2\sqrt{5}\approx -4.472135955$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 10 ki ngā taha e rua.

$$2x^{2}=30+10$$

Tāpirihia te 30 ki te 10, ka 40.

$$2x^{2}=40$$

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=\frac{40}{2}$$

Whakawehea te 40 ki te 2, kia riro ko 20.

$$x^{2}=20$$

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

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 30 mai i ngā taha e rua.

$$2x^{2}-10-30=0$$

Tangohia te 30 i te -10, ka -40.

$$2x^{2}-40=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me -40 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-40\right)}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-40\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\left(-40\right)}}{2\times 2}$$

Whakareatia -8 ki te -40.

$$x=\frac{0±\sqrt{320}}{2\times 2}$$

Tuhia te pūtakerua o te 320.

$$x=\frac{0±8\sqrt{5}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±8\sqrt{5}}{4}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{5}}{4} ina he tāpiri te ±.

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

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{5}}{4} ina he tango te ±.

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

Kua oti te whārite te whakatau.

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