Whakaoti i te 2x^2-46=80

$$2 x ^ { 2 } - 46 = 80$$

Whakaoti mō x

$$x=3\sqrt{7}\approx 7.937253933$$

$$x=-3\sqrt{7}\approx -7.937253933$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 46 ki ngā taha e rua.

$$2x^{2}=80+46$$

Tāpirihia te 80 ki te 46, ka 126.

$$2x^{2}=126$$

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=\frac{126}{2}$$

Whakawehea te 126 ki te 2, kia riro ko 63.

$$x^{2}=63$$

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

$$x=3\sqrt{7} x=-3\sqrt{7}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 80 mai i ngā taha e rua.

$$2x^{2}-46-80=0$$

Tangohia te 80 i te -46, ka -126.

$$2x^{2}-126=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me -126 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-126\right)}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-126\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\left(-126\right)}}{2\times 2}$$

Whakareatia -8 ki te -126.

$$x=\frac{0±\sqrt{1008}}{2\times 2}$$

Tuhia te pūtakerua o te 1008.

$$x=\frac{0±12\sqrt{7}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±12\sqrt{7}}{4}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{7}}{4} ina he tāpiri te ±.

$$x=3\sqrt{7}$$

Nā, me whakaoti te whārite x=\frac{0±12\sqrt{7}}{4} ina he tango te ±.

$$x=-3\sqrt{7}$$

Kua oti te whārite te whakatau.

$$x=3\sqrt{7} x=-3\sqrt{7}$$