Whakaoti i te 36x^2-106=-sqrt{36}

$$36 x ^ { 2 } - 106 = - \sqrt { 36 }$$

Whakaoti mō x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tātaitia te pūtakerua o 36 kia tae ki 6.

$$36x^{2}-106=-6$$

Me tāpiri te 6 ki ngā taha e rua.

$$36x^{2}-106+6=0$$

Tāpirihia te -106 ki te 6, ka -100.

$$36x^{2}-100=0$$

Whakawehea ngā taha e rua ki te 4.

$$9x^{2}-25=0$$

Whakaarohia te 9x^{2}-25. Tuhia anō te 9x^{2}-25 hei \left(3x\right)^{2}-5^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-5\right)\left(3x+5\right)=0$$

Hei kimi otinga whārite, me whakaoti te 3x-5=0 me te 3x+5=0.

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Ngā Upane mā te Kimi Pūtakerua

Tātaitia te pūtakerua o 36 kia tae ki 6.

$$36x^{2}-106=-6$$

Me tāpiri te 106 ki ngā taha e rua.

$$36x^{2}=-6+106$$

Tāpirihia te -6 ki te 106, ka 100.

$$36x^{2}=100$$

Whakawehea ngā taha e rua ki te 36.

$$x^{2}=\frac{100}{36}$$

Whakahekea te hautanga \frac{100}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}=\frac{25}{9}$$

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

$$x=\frac{5}{3} x=-\frac{5}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaitia te pūtakerua o 36 kia tae ki 6.

$$36x^{2}-106=-6$$

Me tāpiri te 6 ki ngā taha e rua.

$$36x^{2}-106+6=0$$

Tāpirihia te -106 ki te 6, ka -100.

$$36x^{2}-100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 36 mō a, 0 mō b, me -100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 36\left(-100\right)}}{2\times 36}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 36\left(-100\right)}}{2\times 36}$$

Whakareatia -4 ki te 36.

$$x=\frac{0±\sqrt{-144\left(-100\right)}}{2\times 36}$$

Whakareatia -144 ki te -100.

$$x=\frac{0±\sqrt{14400}}{2\times 36}$$

Tuhia te pūtakerua o te 14400.

$$x=\frac{0±120}{2\times 36}$$

Whakareatia 2 ki te 36.

$$x=\frac{0±120}{72}$$

Nā, me whakaoti te whārite x=\frac{0±120}{72} ina he tāpiri te ±. Whakahekea te hautanga \frac{120}{72} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 24.

$$x=\frac{5}{3}$$

Nā, me whakaoti te whārite x=\frac{0±120}{72} ina he tango te ±. Whakahekea te hautanga \frac{-120}{72} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 24.

$$x=-\frac{5}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{5}{3} x=-\frac{5}{3}$$