Whakaoti i te 2x^2+4x+2x=0

$$2 { x }^{ 2 } +4x+2x=0$$

Whakaoti mō x

$$x=-3$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(2x+4+2\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 2x+6=0.

$$x=0 x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 4x me 2x, ka 6x.

$$2x^{2}+6x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 6 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}}}{2\times 2}$$

Tuhia te pūtakerua o te 6^{2}.

$$x=\frac{-6±6}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-6±6}{4}$$

Nā, me whakaoti te whārite x=\frac{-6±6}{4} ina he tāpiri te ±. Tāpiri -6 ki te 6.

$$x=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-6±6}{4} ina he tango te ±. Tango 6 mai i -6.

$$x=-\frac{12}{4}$$

Whakawehe -12 ki te 4.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=0 x=-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te 4x me 2x, ka 6x.

$$2x^{2}+6x=0$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+6x}{2}=\frac{0}{2}$$

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

$$x^{2}+\frac{6}{2}x=\frac{0}{2}$$

Whakawehe 6 ki te 2.

$$x^{2}+3x=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$x^{2}+3x=0$$

Whakawehea te 3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{2}. Nā, tāpiria te pūrua o te \frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia \frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+3x+\frac{9}{4}=\frac{9}{4}$$

Tauwehea x^{2}+3x+\frac{9}{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}.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

$$x+\frac{3}{2}=\frac{3}{2} x+\frac{3}{2}=-\frac{3}{2}$$

Me tango \frac{3}{2} mai i ngā taha e rua o te whārite.

$$x=0 x=-3$$