Whakaoti i te 5x^2-2.5x-1.2=0

$$5 { x }^{ 2 } -2.5x-1.2=0$$

Whakaoti mō x

$$x=-0.3$$

$$x=0.8$$

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.

$$5x^{2}-2.5x-1.2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -2.5 mō b, me -1.2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2.5\right)±\sqrt{\left(-2.5\right)^{2}-4\times 5\left(-1.2\right)}}{2\times 5}$$

Pūruatia -2.5 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-2.5\right)±\sqrt{6.25-4\times 5\left(-1.2\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-2.5\right)±\sqrt{6.25-20\left(-1.2\right)}}{2\times 5}$$

Whakareatia -20 ki te -1.2.

$$x=\frac{-\left(-2.5\right)±\sqrt{6.25+24}}{2\times 5}$$

Tāpiri 6.25 ki te 24.

$$x=\frac{-\left(-2.5\right)±\sqrt{30.25}}{2\times 5}$$

Tuhia te pūtakerua o te 30.25.

$$x=\frac{-\left(-2.5\right)±\frac{11}{2}}{2\times 5}$$

Ko te tauaro o -2.5 ko 2.5.

$$x=\frac{2.5±\frac{11}{2}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{2.5±\frac{11}{2}}{10}$$

Nā, me whakaoti te whārite x=\frac{2.5±\frac{11}{2}}{10} ina he tāpiri te ±. Tāpiri 2.5 ki te \frac{11}{2} 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.

$$x=\frac{8}{10}$$

Whakahekea te hautanga \frac{8}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{4}{5}$$

Nā, me whakaoti te whārite x=\frac{2.5±\frac{11}{2}}{10} ina he tango te ±. Tango \frac{11}{2} mai i 2.5 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.

$$x=-\frac{3}{10}$$

Kua oti te whārite te whakatau.

$$x=\frac{4}{5} x=-\frac{3}{10}$$

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.

$$5x^{2}-2.5x-1.2=0$$

Me tāpiri 1.2 ki ngā taha e rua o te whārite.

$$5x^{2}-2.5x-1.2-\left(-1.2\right)=-\left(-1.2\right)$$

Mā te tango i te -1.2 i a ia ake anō ka toe ko te 0.

$$5x^{2}-2.5x=-\left(-1.2\right)$$

Tango -1.2 mai i 0.

$$5x^{2}-2.5x=1.2$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}-2.5x}{5}=\frac{1.2}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$x^{2}+\left(-\frac{2.5}{5}\right)x=\frac{1.2}{5}$$

Whakawehe -2.5 ki te 5.

$$x^{2}-0.5x=\frac{1.2}{5}$$

Whakawehe 1.2 ki te 5.

$$x^{2}-0.5x=0.24$$

Whakawehea te -0.5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -0.25. Nā, tāpiria te pūrua o te -0.25 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-0.5x+\left(-0.25\right)^{2}=0.24+\left(-0.25\right)^{2}$$

Pūruatia -0.25 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-0.5x+0.0625=0.24+0.0625$$

Tāpiri 0.24 ki te 0.0625 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.

$$x^{2}-0.5x+0.0625=0.3025$$

Tauwehea x^{2}-0.5x+0.0625. 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}.

$$\left(x-0.25\right)^{2}=0.3025$$

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

$$\sqrt{\left(x-0.25\right)^{2}}=\sqrt{0.3025}$$

Whakarūnātia.

$$x-0.25=\frac{11}{20} x-0.25=-\frac{11}{20}$$

Me tāpiri 0.25 ki ngā taha e rua o te whārite.

$$x=\frac{4}{5} x=-\frac{3}{10}$$