Whakaoti i te 72x^2+67=99

$$72 { x }^{ 2 } +67=99$$

Whakaoti mō x

$$x=\frac{2}{3}\approx 0.666666667$$

$$x=-\frac{2}{3}\approx -0.666666667$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tangohia te 99 mai i ngā taha e rua.

$$72x^{2}+67-99=0$$

Tangohia te 99 i te 67, ka -32.

$$72x^{2}-32=0$$

Whakawehea ngā taha e rua ki te 8.

$$9x^{2}-4=0$$

Whakaarohia te 9x^{2}-4. Tuhia anō te 9x^{2}-4 hei \left(3x\right)^{2}-2^{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).

$$\left(3x-2\right)\left(3x+2\right)=0$$

Hei kimi otinga whārite, me whakaoti te 3x-2=0 me te 3x+2=0.

$$x=\frac{2}{3} x=-\frac{2}{3}$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 67 mai i ngā taha e rua.

$$72x^{2}=99-67$$

Tangohia te 67 i te 99, ka 32.

$$72x^{2}=32$$

Whakawehea ngā taha e rua ki te 72.

$$x^{2}=\frac{32}{72}$$

Whakahekea te hautanga \frac{32}{72} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$x^{2}=\frac{4}{9}$$

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

$$x=\frac{2}{3} x=-\frac{2}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 99 mai i ngā taha e rua.

$$72x^{2}+67-99=0$$

Tangohia te 99 i te 67, ka -32.

$$72x^{2}-32=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 72 mō a, 0 mō b, me -32 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 72\left(-32\right)}}{2\times 72}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 72\left(-32\right)}}{2\times 72}$$

Whakareatia -4 ki te 72.

$$x=\frac{0±\sqrt{-288\left(-32\right)}}{2\times 72}$$

Whakareatia -288 ki te -32.

$$x=\frac{0±\sqrt{9216}}{2\times 72}$$

Tuhia te pūtakerua o te 9216.

$$x=\frac{0±96}{2\times 72}$$

Whakareatia 2 ki te 72.

$$x=\frac{0±96}{144}$$

Nā, me whakaoti te whārite x=\frac{0±96}{144} ina he tāpiri te ±. Whakahekea te hautanga \frac{96}{144} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 48.

$$x=\frac{2}{3}$$

Nā, me whakaoti te whārite x=\frac{0±96}{144} ina he tango te ±. Whakahekea te hautanga \frac{-96}{144} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 48.

$$x=-\frac{2}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{2}{3} x=-\frac{2}{3}$$