Whakaoti i te x^2=0.5+1.5x

$$x ^ { 2 } = 0.5 + 1.5 x$$

Whakaoti mō x

$$x = \frac{\sqrt{17} + 3}{4} \approx 1.780776406$$

$$x=\frac{3-\sqrt{17}}{4}\approx -0.280776406$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 0.5 mai i ngā taha e rua.

$$x^{2}-0.5=1.5x$$

Tangohia te 1.5x mai i ngā taha e rua.

$$x^{2}-0.5-1.5x=0$$

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.

$$x^{2}-1.5x-0.5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -1.5 mō b, me -0.5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1.5\right)±\sqrt{\left(-1.5\right)^{2}-4\left(-0.5\right)}}{2}$$

Pūruatia -1.5 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-1.5\right)±\sqrt{2.25-4\left(-0.5\right)}}{2}$$

Whakareatia -4 ki te -0.5.

$$x=\frac{-\left(-1.5\right)±\sqrt{2.25+2}}{2}$$

Tāpiri 2.25 ki te 2.

$$x=\frac{-\left(-1.5\right)±\sqrt{4.25}}{2}$$

Tuhia te pūtakerua o te 4.25.

$$x=\frac{-\left(-1.5\right)±\frac{\sqrt{17}}{2}}{2}$$

Ko te tauaro o -1.5 ko 1.5.

$$x=\frac{1.5±\frac{\sqrt{17}}{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{1.5±\frac{\sqrt{17}}{2}}{2} ina he tāpiri te ±. Tāpiri 1.5 ki te \frac{\sqrt{17}}{2}.

$$x=\frac{\sqrt{17}+3}{2\times 2}$$

Whakawehe \frac{3+\sqrt{17}}{2} ki te 2.

$$x=\frac{\sqrt{17}+3}{4}$$

Nā, me whakaoti te whārite x=\frac{1.5±\frac{\sqrt{17}}{2}}{2} ina he tango te ±. Tango \frac{\sqrt{17}}{2} mai i 1.5.

$$x=\frac{3-\sqrt{17}}{2\times 2}$$

Whakawehe \frac{3-\sqrt{17}}{2} ki te 2.

$$x=\frac{3-\sqrt{17}}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{17}+3}{4} x=\frac{3-\sqrt{17}}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 1.5x mai i ngā taha e rua.

$$x^{2}-1.5x=0.5$$

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.

$$x^{2}-1.5x=\frac{1}{2}$$

Whakawehea te -1.5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -0.75. Nā, tāpiria te pūrua o te -0.75 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-1.5x+\left(-0.75\right)^{2}=\frac{1}{2}+\left(-0.75\right)^{2}$$

Pūruatia -0.75 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-1.5x+0.5625=\frac{1}{2}+0.5625$$

Tāpiri \frac{1}{2} ki te 0.5625 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.

$$x^{2}-1.5x+0.5625=\frac{17}{16}$$

Tauwehea x^{2}-1.5x+0.5625. 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}.

$$\left(x-0.75\right)^{2}=\frac{17}{16}$$

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

$$\sqrt{\left(x-0.75\right)^{2}}=\sqrt{\frac{17}{16}}$$

Whakarūnātia.

$$x-0.75=\frac{\sqrt{17}}{4} x-0.75=-\frac{\sqrt{17}}{4}$$

Me tāpiri 0.75 ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{17}+3}{4} x=\frac{3-\sqrt{17}}{4}$$