Whakaoti i te a^2+3a-2a=0

$${ a }^{ 2 } +3a-2a=0$$

Whakaoti mō a

$$a=-1$$

$$a=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te a.

$$a\left(a+3-2\right)=0$$

Hei kimi otinga whārite, me whakaoti te a=0 me te a+1=0.

$$a=0 a=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 3a me -2a, ka a.

$$a^{2}+a=0$$

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

$$a=\frac{-1±\sqrt{1^{2}}}{2}$$

Tuhia te pūtakerua o te 1^{2}.

$$a=\frac{-1±1}{2}$$

Nā, me whakaoti te whārite a=\frac{-1±1}{2} ina he tāpiri te ±. Tāpiri -1 ki te 1.

$$a=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$a=0$$

Nā, me whakaoti te whārite a=\frac{-1±1}{2} ina he tango te ±. Tango 1 mai i -1.

$$a=-\frac{2}{2}$$

Whakawehe -2 ki te 2.

$$a=-1$$

Kua oti te whārite te whakatau.

$$a=0 a=-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te 3a me -2a, ka a.

$$a^{2}+a=0$$

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

$$a^{2}+a+\left(\frac{1}{2}\right)^{2}=\left(\frac{1}{2}\right)^{2}$$

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$a^{2}+a+\frac{1}{4}=\frac{1}{4}$$

Tauwehea a^{2}+a+\frac{1}{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}.

$$\left(a+\frac{1}{2}\right)^{2}=\frac{1}{4}$$

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

$$\sqrt{\left(a+\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Whakarūnātia.

$$a+\frac{1}{2}=\frac{1}{2} a+\frac{1}{2}=-\frac{1}{2}$$

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$a=0 a=-1$$