Whakaoti i te 11x^2-10=67

$$11 { x }^{ 2 } -10=67$$

Whakaoti mō x

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 10 ki ngā taha e rua.

$$11x^{2}=67+10$$

Tāpirihia te 67 ki te 10, ka 77.

$$11x^{2}=77$$

Whakawehea ngā taha e rua ki te 11.

$$x^{2}=\frac{77}{11}$$

Whakawehea te 77 ki te 11, kia riro ko 7.

$$x^{2}=7$$

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

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 67 mai i ngā taha e rua.

$$11x^{2}-10-67=0$$

Tangohia te 67 i te -10, ka -77.

$$11x^{2}-77=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 11 mō a, 0 mō b, me -77 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 11\left(-77\right)}}{2\times 11}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 11\left(-77\right)}}{2\times 11}$$

Whakareatia -4 ki te 11.

$$x=\frac{0±\sqrt{-44\left(-77\right)}}{2\times 11}$$

Whakareatia -44 ki te -77.

$$x=\frac{0±\sqrt{3388}}{2\times 11}$$

Tuhia te pūtakerua o te 3388.

$$x=\frac{0±22\sqrt{7}}{2\times 11}$$

Whakareatia 2 ki te 11.

$$x=\frac{0±22\sqrt{7}}{22}$$

Nā, me whakaoti te whārite x=\frac{0±22\sqrt{7}}{22} ina he tāpiri te ±.

$$x=\sqrt{7}$$

Nā, me whakaoti te whārite x=\frac{0±22\sqrt{7}}{22} ina he tango te ±.

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

Kua oti te whārite te whakatau.

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