Whakaoti i te x^2-1/10x-3/10=0

$${ x }^{ 2 } - \frac{ 1 }{ 10 } x- \frac{ 3 }{ 10 } =0$$

Whakaoti mō x

$$x=-\frac{1}{2}=-0.5$$

$$x=\frac{3}{5}=0.6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x^{2}-\frac{1}{10}x-\frac{3}{10}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -\frac{1}{10} mō b, me -\frac{3}{10} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{1}{10}\right)±\sqrt{\left(-\frac{1}{10}\right)^{2}-4\left(-\frac{3}{10}\right)}}{2}$$

Pūruatia -\frac{1}{10} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-\frac{1}{10}\right)±\sqrt{\frac{1}{100}-4\left(-\frac{3}{10}\right)}}{2}$$

Whakareatia -4 ki te -\frac{3}{10}.

$$x=\frac{-\left(-\frac{1}{10}\right)±\sqrt{\frac{1}{100}+\frac{6}{5}}}{2}$$

Tāpiri \frac{1}{100} ki te \frac{6}{5} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{-\left(-\frac{1}{10}\right)±\sqrt{\frac{121}{100}}}{2}$$

Tuhia te pūtakerua o te \frac{121}{100}.

$$x=\frac{-\left(-\frac{1}{10}\right)±\frac{11}{10}}{2}$$

Ko te tauaro o -\frac{1}{10} ko \frac{1}{10}.

$$x=\frac{\frac{1}{10}±\frac{11}{10}}{2}$$

Nā, me whakaoti te whārite x=\frac{\frac{1}{10}±\frac{11}{10}}{2} ina he tāpiri te ±. Tāpiri \frac{1}{10} ki te \frac{11}{10} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{\frac{6}{5}}{2}$$

Whakawehe \frac{6}{5} ki te 2.

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

Nā, me whakaoti te whārite x=\frac{\frac{1}{10}±\frac{11}{10}}{2} ina he tango te ±. Tango \frac{11}{10} mai i \frac{1}{10} mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=-\frac{1}{2}$$

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$x^{2}-\frac{1}{10}x-\frac{3}{10}=0$$

Me tāpiri \frac{3}{10} ki ngā taha e rua o te whārite.

$$x^{2}-\frac{1}{10}x-\frac{3}{10}-\left(-\frac{3}{10}\right)=-\left(-\frac{3}{10}\right)$$

Mā te tango i te -\frac{3}{10} i a ia ake anō ka toe ko te 0.

$$x^{2}-\frac{1}{10}x=-\left(-\frac{3}{10}\right)$$

Tango -\frac{3}{10} mai i 0.

$$x^{2}-\frac{1}{10}x=\frac{3}{10}$$

Whakawehea te -\frac{1}{10}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{20}. Nā, tāpiria te pūrua o te -\frac{1}{20} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{10}x+\left(-\frac{1}{20}\right)^{2}=\frac{3}{10}+\left(-\frac{1}{20}\right)^{2}$$

Pūruatia -\frac{1}{20} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{10}x+\frac{1}{400}=\frac{3}{10}+\frac{1}{400}$$

Tāpiri \frac{3}{10} ki te \frac{1}{400} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{1}{10}x+\frac{1}{400}=\frac{121}{400}$$

Tauwehea x^{2}-\frac{1}{10}x+\frac{1}{400}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{20}\right)^{2}=\frac{121}{400}$$

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

$$\sqrt{\left(x-\frac{1}{20}\right)^{2}}=\sqrt{\frac{121}{400}}$$

Whakarūnātia.

$$x-\frac{1}{20}=\frac{11}{20} x-\frac{1}{20}=-\frac{11}{20}$$

Me tāpiri \frac{1}{20} ki ngā taha e rua o te whārite.

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