Whakaoti i te 10x^2=2x+3

$$10 x ^ { 2 } = 2 x + 3$$

Whakaoti mō x

$$x=\frac{\sqrt{31}+1}{10}\approx 0.656776436$$

$$x=\frac{1-\sqrt{31}}{10}\approx -0.456776436$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 2x mai i ngā taha e rua.

$$10x^{2}-2x=3$$

Tangohia te 3 mai i ngā taha e rua.

$$10x^{2}-2x-3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 10 mō a, -2 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 10\left(-3\right)}}{2\times 10}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times 10\left(-3\right)}}{2\times 10}$$

Whakareatia -4 ki te 10.

$$x=\frac{-\left(-2\right)±\sqrt{4-40\left(-3\right)}}{2\times 10}$$

Whakareatia -40 ki te -3.

$$x=\frac{-\left(-2\right)±\sqrt{4+120}}{2\times 10}$$

Tāpiri 4 ki te 120.

$$x=\frac{-\left(-2\right)±\sqrt{124}}{2\times 10}$$

Tuhia te pūtakerua o te 124.

$$x=\frac{-\left(-2\right)±2\sqrt{31}}{2\times 10}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±2\sqrt{31}}{2\times 10}$$

Whakareatia 2 ki te 10.

$$x=\frac{2±2\sqrt{31}}{20}$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{31}}{20} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{31}.

$$x=\frac{2\sqrt{31}+2}{20}$$

Whakawehe 2+2\sqrt{31} ki te 20.

$$x=\frac{\sqrt{31}+1}{10}$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{31}}{20} ina he tango te ±. Tango 2\sqrt{31} mai i 2.

$$x=\frac{2-2\sqrt{31}}{20}$$

Whakawehe 2-2\sqrt{31} ki te 20.

$$x=\frac{1-\sqrt{31}}{10}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{31}+1}{10} x=\frac{1-\sqrt{31}}{10}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 2x mai i ngā taha e rua.

$$10x^{2}-2x=3$$

Whakawehea ngā taha e rua ki te 10.

$$\frac{10x^{2}-2x}{10}=\frac{3}{10}$$

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

$$x^{2}+\left(-\frac{2}{10}\right)x=\frac{3}{10}$$

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

$$x^{2}-\frac{1}{5}x=\frac{3}{10}$$

Whakawehea te -\frac{1}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{10}. Nā, tāpiria te pūrua o te -\frac{1}{10} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{5}x+\left(-\frac{1}{10}\right)^{2}=\frac{3}{10}+\left(-\frac{1}{10}\right)^{2}$$

Pūruatia -\frac{1}{10} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{5}x+\frac{1}{100}=\frac{3}{10}+\frac{1}{100}$$

Tāpiri \frac{3}{10} ki te \frac{1}{100} 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.

$$x^{2}-\frac{1}{5}x+\frac{1}{100}=\frac{31}{100}$$

Tauwehea x^{2}-\frac{1}{5}x+\frac{1}{100}. 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}.

$$\left(x-\frac{1}{10}\right)^{2}=\frac{31}{100}$$

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

$$\sqrt{\left(x-\frac{1}{10}\right)^{2}}=\sqrt{\frac{31}{100}}$$

Whakarūnātia.

$$x-\frac{1}{10}=\frac{\sqrt{31}}{10} x-\frac{1}{10}=-\frac{\sqrt{31}}{10}$$

Me tāpiri \frac{1}{10} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{31}+1}{10} x=\frac{1-\sqrt{31}}{10}$$