Whakaoti i te 2*x^2=x+12.3

$$2 \cdot x ^ { 2 } = x + 12.3$$

Whakaoti mō x

$$x=\frac{\sqrt{2485}}{20}+0.25\approx 2.742488716$$

$$x=-\frac{\sqrt{2485}}{20}+0.25\approx -2.242488716$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x mai i ngā taha e rua.

$$2x^{2}-x=12.3$$

Tangohia te 12.3 mai i ngā taha e rua.

$$2x^{2}-x-12.3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -1 mō b, me -12.3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 2\left(-12.3\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-1\right)±\sqrt{1-8\left(-12.3\right)}}{2\times 2}$$

Whakareatia -8 ki te -12.3.

$$x=\frac{-\left(-1\right)±\sqrt{1+98.4}}{2\times 2}$$

Tāpiri 1 ki te 98.4.

$$x=\frac{-\left(-1\right)±\sqrt{99.4}}{2\times 2}$$

Tuhia te pūtakerua o te 99.4.

$$x=\frac{-\left(-1\right)±\frac{\sqrt{2485}}{5}}{2\times 2}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±\frac{\sqrt{2485}}{5}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{1±\frac{\sqrt{2485}}{5}}{4}$$

Nā, me whakaoti te whārite x=\frac{1±\frac{\sqrt{2485}}{5}}{4} ina he tāpiri te ±. Tāpiri 1 ki te \frac{\sqrt{2485}}{5}.

$$x=\frac{\frac{\sqrt{2485}}{5}+1}{4}$$

Whakawehe 1+\frac{\sqrt{2485}}{5} ki te 4.

$$x=\frac{\sqrt{2485}}{20}+\frac{1}{4}$$

Nā, me whakaoti te whārite x=\frac{1±\frac{\sqrt{2485}}{5}}{4} ina he tango te ±. Tango \frac{\sqrt{2485}}{5} mai i 1.

$$x=\frac{-\frac{\sqrt{2485}}{5}+1}{4}$$

Whakawehe 1-\frac{\sqrt{2485}}{5} ki te 4.

$$x=-\frac{\sqrt{2485}}{20}+\frac{1}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{2485}}{20}+\frac{1}{4} x=-\frac{\sqrt{2485}}{20}+\frac{1}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x mai i ngā taha e rua.

$$2x^{2}-x=12.3$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-x}{2}=\frac{12.3}{2}$$

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

$$x^{2}-\frac{1}{2}x=\frac{12.3}{2}$$

Whakawehe 12.3 ki te 2.

$$x^{2}-\frac{1}{2}x=6.15$$

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.

$$x^{2}-\frac{1}{2}x+\left(-\frac{1}{4}\right)^{2}=6.15+\left(-\frac{1}{4}\right)^{2}$$

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

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=6.15+\frac{1}{16}$$

Tāpiri 6.15 ki te \frac{1}{16} 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.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{497}{80}$$

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}.

$$\left(x-\frac{1}{4}\right)^{2}=\frac{497}{80}$$

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

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{497}{80}}$$

Whakarūnātia.

$$x-\frac{1}{4}=\frac{\sqrt{2485}}{20} x-\frac{1}{4}=-\frac{\sqrt{2485}}{20}$$

Me tāpiri \frac{1}{4} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{2485}}{20}+\frac{1}{4} x=-\frac{\sqrt{2485}}{20}+\frac{1}{4}$$