Whakaoti i te 2x^2-5.5x+3=0

$$2 { x }^{ 2 } -5.5x+3=0$$

Whakaoti mō x

$$x=2$$

$$x=0.75$$

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.

$$2x^{2}-5.5x+3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -5.5 mō b, me 3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5.5\right)±\sqrt{\left(-5.5\right)^{2}-4\times 2\times 3}}{2\times 2}$$

Pūruatia -5.5 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-5.5\right)±\sqrt{30.25-4\times 2\times 3}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-5.5\right)±\sqrt{30.25-8\times 3}}{2\times 2}$$

Whakareatia -8 ki te 3.

$$x=\frac{-\left(-5.5\right)±\sqrt{30.25-24}}{2\times 2}$$

Tāpiri 30.25 ki te -24.

$$x=\frac{-\left(-5.5\right)±\sqrt{6.25}}{2\times 2}$$

Tuhia te pūtakerua o te 6.25.

$$x=\frac{-\left(-5.5\right)±\frac{5}{2}}{2\times 2}$$

Ko te tauaro o -5.5 ko 5.5.

$$x=\frac{5.5±\frac{5}{2}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{5.5±\frac{5}{2}}{4}$$

Nā, me whakaoti te whārite x=\frac{5.5±\frac{5}{2}}{4} ina he tāpiri te ±. Tāpiri 5.5 ki te \frac{5}{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.

$$x=\frac{8}{4}$$

Whakawehe 8 ki te 4.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{5.5±\frac{5}{2}}{4} ina he tango te ±. Tango \frac{5}{2} mai i 5.5 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.

$$x=\frac{3}{4}$$

Kua oti te whārite te whakatau.

$$x=2 x=\frac{3}{4}$$

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.

$$2x^{2}-5.5x+3=0$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$2x^{2}-5.5x+3-3=-3$$

Mā te tango i te 3 i a ia ake anō ka toe ko te 0.

$$2x^{2}-5.5x=-3$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-5.5x}{2}=-\frac{3}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\left(-\frac{5.5}{2}\right)x=-\frac{3}{2}$$

Whakawehe -5.5 ki te 2.

$$x^{2}-2.75x=-\frac{3}{2}$$

Whakawehea te -2.75, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1.375. Nā, tāpiria te pūrua o te -1.375 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-2.75x+\left(-1.375\right)^{2}=-\frac{3}{2}+\left(-1.375\right)^{2}$$

Pūruatia -1.375 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-2.75x+1.890625=-\frac{3}{2}+1.890625$$

Tāpiri -\frac{3}{2} ki te 1.890625 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.

$$x^{2}-2.75x+1.890625=\frac{25}{64}$$

Tauwehea x^{2}-2.75x+1.890625. 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}.

$$\left(x-1.375\right)^{2}=\frac{25}{64}$$

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

$$\sqrt{\left(x-1.375\right)^{2}}=\sqrt{\frac{25}{64}}$$

Whakarūnātia.

$$x-1.375=\frac{5}{8} x-1.375=-\frac{5}{8}$$

Me tāpiri 1.375 ki ngā taha e rua o te whārite.

$$x=2 x=\frac{3}{4}$$