Whakaoti i te xdiv10+2xdiv10x=0.06x+3

$$x \div 10+2x \div 10x=0.06x+3$$

Whakaoti mō x

$$x = \frac{\sqrt{1501} - 1}{10} \approx 3.774274126$$

$$x=\frac{-\sqrt{1501}-1}{10}\approx -3.974274126$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$x+2xx=0.6x+30$$

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

$$x+2x^{2}=0.6x+30$$

Tangohia te 0.6x mai i ngā taha e rua.

$$x+2x^{2}-0.6x=30$$

Pahekotia te x me -0.6x, ka 0.4x.

$$0.4x+2x^{2}=30$$

Tangohia te 30 mai i ngā taha e rua.

$$0.4x+2x^{2}-30=0$$

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.

$$2x^{2}+0.4x-30=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0.4 mō b, me -30 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.4±\sqrt{0.4^{2}-4\times 2\left(-30\right)}}{2\times 2}$$

Pūruatia 0.4 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-0.4±\sqrt{0.16-4\times 2\left(-30\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-0.4±\sqrt{0.16-8\left(-30\right)}}{2\times 2}$$

Whakareatia -8 ki te -30.

$$x=\frac{-0.4±\sqrt{0.16+240}}{2\times 2}$$

Tāpiri 0.16 ki te 240.

$$x=\frac{-0.4±\sqrt{240.16}}{2\times 2}$$

Tuhia te pūtakerua o te 240.16.

$$x=\frac{-0.4±\frac{2\sqrt{1501}}{5}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-0.4±\frac{2\sqrt{1501}}{5}}{4}$$

Nā, me whakaoti te whārite x=\frac{-0.4±\frac{2\sqrt{1501}}{5}}{4} ina he tāpiri te ±. Tāpiri -0.4 ki te \frac{2\sqrt{1501}}{5}.

$$x=\frac{2\sqrt{1501}-2}{4\times 5}$$

Whakawehe \frac{-2+2\sqrt{1501}}{5} ki te 4.

$$x=\frac{\sqrt{1501}-1}{10}$$

Nā, me whakaoti te whārite x=\frac{-0.4±\frac{2\sqrt{1501}}{5}}{4} ina he tango te ±. Tango \frac{2\sqrt{1501}}{5} mai i -0.4.

$$x=\frac{-2\sqrt{1501}-2}{4\times 5}$$

Whakawehe \frac{-2-2\sqrt{1501}}{5} ki te 4.

$$x=\frac{-\sqrt{1501}-1}{10}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{1501}-1}{10} x=\frac{-\sqrt{1501}-1}{10}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$x+2xx=0.6x+30$$

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

$$x+2x^{2}=0.6x+30$$

Tangohia te 0.6x mai i ngā taha e rua.

$$x+2x^{2}-0.6x=30$$

Pahekotia te x me -0.6x, ka 0.4x.

$$0.4x+2x^{2}=30$$

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.

$$2x^{2}+0.4x=30$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+0.4x}{2}=\frac{30}{2}$$

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

$$x^{2}+\frac{0.4}{2}x=\frac{30}{2}$$

Whakawehe 0.4 ki te 2.

$$x^{2}+0.2x=\frac{30}{2}$$

Whakawehe 30 ki te 2.

$$x^{2}+0.2x=15$$

Whakawehea te 0.2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 0.1. Nā, tāpiria te pūrua o te 0.1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+0.2x+0.1^{2}=15+0.1^{2}$$

Pūruatia 0.1 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+0.2x+0.01=15+0.01$$

Tāpiri 15 ki te 0.01.

$$x^{2}+0.2x+0.01=15.01$$

Tauwehea x^{2}+0.2x+0.01. 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}.

$$\left(x+0.1\right)^{2}=15.01$$

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

$$\sqrt{\left(x+0.1\right)^{2}}=\sqrt{15.01}$$

Whakarūnātia.

$$x+0.1=\frac{\sqrt{1501}}{10} x+0.1=-\frac{\sqrt{1501}}{10}$$

Me tango 0.1 mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{1501}-1}{10} x=\frac{-\sqrt{1501}-1}{10}$$