Whakaoti i te (x)=x^2-2x/2+3

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

Whakaoti mō x

$$x=7$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tāpirihia te 2 ki te 3, ka 5.

$$x=\frac{x^{2}-2x}{5}$$

Whakawehea ia wā o x^{2}-2x ki te 5, kia riro ko \frac{1}{5}x^{2}-\frac{2}{5}x.

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

Tangohia te \frac{1}{5}x^{2} mai i ngā taha e rua.

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

Me tāpiri te \frac{2}{5}x ki ngā taha e rua.

$$x-\frac{1}{5}x^{2}+\frac{2}{5}x=0$$

Pahekotia te x me \frac{2}{5}x, ka \frac{7}{5}x.

$$\frac{7}{5}x-\frac{1}{5}x^{2}=0$$

Tauwehea te x.

$$x\left(\frac{7}{5}-\frac{1}{5}x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te \frac{7-x}{5}=0.

$$x=0 x=7$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 2 ki te 3, ka 5.

$$x=\frac{x^{2}-2x}{5}$$

Whakawehea ia wā o x^{2}-2x ki te 5, kia riro ko \frac{1}{5}x^{2}-\frac{2}{5}x.

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

Tangohia te \frac{1}{5}x^{2} mai i ngā taha e rua.

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

Me tāpiri te \frac{2}{5}x ki ngā taha e rua.

$$x-\frac{1}{5}x^{2}+\frac{2}{5}x=0$$

Pahekotia te x me \frac{2}{5}x, ka \frac{7}{5}x.

$$\frac{7}{5}x-\frac{1}{5}x^{2}=0$$

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.

$$-\frac{1}{5}x^{2}+\frac{7}{5}x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -\frac{1}{5} mō a, \frac{7}{5} mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{7}{5}±\sqrt{\left(\frac{7}{5}\right)^{2}}}{2\left(-\frac{1}{5}\right)}$$

Tuhia te pūtakerua o te \left(\frac{7}{5}\right)^{2}.

$$x=\frac{-\frac{7}{5}±\frac{7}{5}}{2\left(-\frac{1}{5}\right)}$$

Whakareatia 2 ki te -\frac{1}{5}.

$$x=\frac{-\frac{7}{5}±\frac{7}{5}}{-\frac{2}{5}}$$

Nā, me whakaoti te whārite x=\frac{-\frac{7}{5}±\frac{7}{5}}{-\frac{2}{5}} ina he tāpiri te ±. Tāpiri -\frac{7}{5} ki te \frac{7}{5} 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.

$$x=\frac{0}{-\frac{2}{5}}$$

Whakawehe 0 ki te -\frac{2}{5} mā te whakarea 0 ki te tau huripoki o -\frac{2}{5}.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-\frac{7}{5}±\frac{7}{5}}{-\frac{2}{5}} ina he tango te ±. Tango \frac{7}{5} mai i -\frac{7}{5} mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=-\frac{\frac{14}{5}}{-\frac{2}{5}}$$

Whakawehe -\frac{14}{5} ki te -\frac{2}{5} mā te whakarea -\frac{14}{5} ki te tau huripoki o -\frac{2}{5}.

$$x=7$$

Kua oti te whārite te whakatau.

$$x=0 x=7$$

Ngā Upane mō te Whakaoti i te Pūrua

Tāpirihia te 2 ki te 3, ka 5.

$$x=\frac{x^{2}-2x}{5}$$

Whakawehea ia wā o x^{2}-2x ki te 5, kia riro ko \frac{1}{5}x^{2}-\frac{2}{5}x.

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

Tangohia te \frac{1}{5}x^{2} mai i ngā taha e rua.

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

Me tāpiri te \frac{2}{5}x ki ngā taha e rua.

$$x-\frac{1}{5}x^{2}+\frac{2}{5}x=0$$

Pahekotia te x me \frac{2}{5}x, ka \frac{7}{5}x.

$$\frac{7}{5}x-\frac{1}{5}x^{2}=0$$

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.

$$-\frac{1}{5}x^{2}+\frac{7}{5}x=0$$

Me whakarea ngā taha e rua ki te -5.

$$\frac{-\frac{1}{5}x^{2}+\frac{7}{5}x}{-\frac{1}{5}}=\frac{0}{-\frac{1}{5}}$$

Mā te whakawehe ki te -\frac{1}{5} ka wetekia te whakareanga ki te -\frac{1}{5}.

$$x^{2}+\frac{\frac{7}{5}}{-\frac{1}{5}}x=\frac{0}{-\frac{1}{5}}$$

Whakawehe \frac{7}{5} ki te -\frac{1}{5} mā te whakarea \frac{7}{5} ki te tau huripoki o -\frac{1}{5}.

$$x^{2}-7x=\frac{0}{-\frac{1}{5}}$$

Whakawehe 0 ki te -\frac{1}{5} mā te whakarea 0 ki te tau huripoki o -\frac{1}{5}.

$$x^{2}-7x=0$$

Whakawehea te -7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{2}. Nā, tāpiria te pūrua o te -\frac{7}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Pūruatia -\frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-7x+\frac{49}{4}=\frac{49}{4}$$

Tauwehea x^{2}-7x+\frac{49}{4}. 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}.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

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

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Whakarūnātia.

$$x-\frac{7}{2}=\frac{7}{2} x-\frac{7}{2}=-\frac{7}{2}$$

Me tāpiri \frac{7}{2} ki ngā taha e rua o te whārite.

$$x=7 x=0$$