Whakaoti i te 10x^2-6.5x+0.75=0

$$10 x ^ { 2 } - 6.5 x + 0.75 = 0$$

Whakaoti mō x

$$x=0.15$$

$$x=0.5$$

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.

$$10x^{2}-6.5x+0.75=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 10 mō a, -6.5 mō b, me 0.75 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6.5\right)±\sqrt{\left(-6.5\right)^{2}-4\times 10\times 0.75}}{2\times 10}$$

Pūruatia -6.5 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-6.5\right)±\sqrt{42.25-4\times 10\times 0.75}}{2\times 10}$$

Whakareatia -4 ki te 10.

$$x=\frac{-\left(-6.5\right)±\sqrt{42.25-40\times 0.75}}{2\times 10}$$

Whakareatia -40 ki te 0.75.

$$x=\frac{-\left(-6.5\right)±\sqrt{42.25-30}}{2\times 10}$$

Tāpiri 42.25 ki te -30.

$$x=\frac{-\left(-6.5\right)±\sqrt{12.25}}{2\times 10}$$

Tuhia te pūtakerua o te 12.25.

$$x=\frac{-\left(-6.5\right)±\frac{7}{2}}{2\times 10}$$

Ko te tauaro o -6.5 ko 6.5.

$$x=\frac{6.5±\frac{7}{2}}{2\times 10}$$

Whakareatia 2 ki te 10.

$$x=\frac{6.5±\frac{7}{2}}{20}$$

Nā, me whakaoti te whārite x=\frac{6.5±\frac{7}{2}}{20} ina he tāpiri te ±. Tāpiri 6.5 ki te \frac{7}{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.

$$x=\frac{10}{20}$$

Whakahekea te hautanga \frac{10}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

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

Nā, me whakaoti te whārite x=\frac{6.5±\frac{7}{2}}{20} ina he tango te ±. Tango \frac{7}{2} mai i 6.5 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.

$$x=\frac{3}{20}$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{2} x=\frac{3}{20}$$

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.

$$10x^{2}-6.5x+0.75=0$$

Me tango 0.75 mai i ngā taha e rua o te whārite.

$$10x^{2}-6.5x+0.75-0.75=-0.75$$

Mā te tango i te 0.75 i a ia ake anō ka toe ko te 0.

$$10x^{2}-6.5x=-0.75$$

Whakawehea ngā taha e rua ki te 10.

$$\frac{10x^{2}-6.5x}{10}=-\frac{0.75}{10}$$

Mā te whakawehe ki te 10 ka wetekia te whakareanga ki te 10.

$$x^{2}+\left(-\frac{6.5}{10}\right)x=-\frac{0.75}{10}$$

Whakawehe -6.5 ki te 10.

$$x^{2}-0.65x=-\frac{0.75}{10}$$

Whakawehe -0.75 ki te 10.

$$x^{2}-0.65x=-0.075$$

Whakawehea te -0.65, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -0.325. Nā, tāpiria te pūrua o te -0.325 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-0.65x+\left(-0.325\right)^{2}=-0.075+\left(-0.325\right)^{2}$$

Pūruatia -0.325 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-0.65x+0.105625=-0.075+0.105625$$

Tāpiri -0.075 ki te 0.105625 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.

$$x^{2}-0.65x+0.105625=0.030625$$

Tauwehea x^{2}-0.65x+0.105625. 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}.

$$\left(x-0.325\right)^{2}=0.030625$$

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

$$\sqrt{\left(x-0.325\right)^{2}}=\sqrt{0.030625}$$

Whakarūnātia.

$$x-0.325=\frac{7}{40} x-0.325=-\frac{7}{40}$$

Me tāpiri 0.325 ki ngā taha e rua o te whārite.

$$x=\frac{1}{2} x=\frac{3}{20}$$