Whakaoti i te xdiv10+2xdiv10x=006x+3

$$x \div 10+2x \div 10x=006x+3$$

Whakaoti mō x

$$x = \frac{\sqrt{241} - 1}{4} \approx 3.631043674$$

$$x=\frac{-\sqrt{241}-1}{4}\approx -4.131043674$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 10.

$$x+2xx=0\times 0\times 6x+30$$

Whakareatia te x ki te x, ka x^{2}.

$$x+2x^{2}=0\times 0\times 6x+30$$

Whakareatia te 0 ki te 0, ka 0.

$$x+2x^{2}=0\times 6x+30$$

Whakareatia te 0 ki te 6, ka 0.

$$x+2x^{2}=0x+30$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$x+2x^{2}=0+30$$

Tāpirihia te 0 ki te 30, ka 30.

$$x+2x^{2}=30$$

Tangohia te 30 mai i ngā taha e rua.

$$x+2x^{2}-30=0$$

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.

$$2x^{2}+x-30=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 1 mō b, me -30 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\times 2\left(-30\right)}}{2\times 2}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\times 2\left(-30\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-1±\sqrt{1-8\left(-30\right)}}{2\times 2}$$

Whakareatia -8 ki te -30.

$$x=\frac{-1±\sqrt{1+240}}{2\times 2}$$

Tāpiri 1 ki te 240.

$$x=\frac{-1±\sqrt{241}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-1±\sqrt{241}}{4}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{241}}{4} ina he tāpiri te ±. Tāpiri -1 ki te \sqrt{241}.

$$x=\frac{\sqrt{241}-1}{4}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{241}}{4} ina he tango te ±. Tango \sqrt{241} mai i -1.

$$x=\frac{-\sqrt{241}-1}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{241}-1}{4} x=\frac{-\sqrt{241}-1}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 10.

$$x+2xx=0\times 0\times 6x+30$$

Whakareatia te x ki te x, ka x^{2}.

$$x+2x^{2}=0\times 0\times 6x+30$$

Whakareatia te 0 ki te 0, ka 0.

$$x+2x^{2}=0\times 6x+30$$

Whakareatia te 0 ki te 6, ka 0.

$$x+2x^{2}=0x+30$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$x+2x^{2}=0+30$$

Tāpirihia te 0 ki te 30, ka 30.

$$x+2x^{2}=30$$

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.

$$2x^{2}+x=30$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+x}{2}=\frac{30}{2}$$

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

$$x^{2}+\frac{1}{2}x=\frac{30}{2}$$

Whakawehe 30 ki te 2.

$$x^{2}+\frac{1}{2}x=15$$

Whakawehea te \frac{1}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{4}. Nā, tāpiria te pūrua o te \frac{1}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{1}{2}x+\left(\frac{1}{4}\right)^{2}=15+\left(\frac{1}{4}\right)^{2}$$

Pūruatia \frac{1}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{1}{2}x+\frac{1}{16}=15+\frac{1}{16}$$

Tāpiri 15 ki te \frac{1}{16}.

$$x^{2}+\frac{1}{2}x+\frac{1}{16}=\frac{241}{16}$$

Tauwehea x^{2}+\frac{1}{2}x+\frac{1}{16}. 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}.

$$\left(x+\frac{1}{4}\right)^{2}=\frac{241}{16}$$

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

$$\sqrt{\left(x+\frac{1}{4}\right)^{2}}=\sqrt{\frac{241}{16}}$$

Whakarūnātia.

$$x+\frac{1}{4}=\frac{\sqrt{241}}{4} x+\frac{1}{4}=-\frac{\sqrt{241}}{4}$$

Me tango \frac{1}{4} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{241}-1}{4} x=\frac{-\sqrt{241}-1}{4}$$