Whakaoti i te -2x^2=3x

$$- 2 x ^ { 2 } = 3 x$$

Whakaoti mō x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 3x mai i ngā taha e rua.

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

Tauwehea te x.

$$x\left(-2x-3\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -2x-3=0.

$$x=0 x=-\frac{3}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 3x mai i ngā taha e rua.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, -3 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te \left(-3\right)^{2}.

$$x=\frac{-\left(-3\right)±3}{2\left(-2\right)}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±3}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{3±3}{-4}$$

Nā, me whakaoti te whārite x=\frac{3±3}{-4} ina he tāpiri te ±. Tāpiri 3 ki te 3.

$$x=\frac{6}{-4}$$

Whakahekea te hautanga \frac{6}{-4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Nā, me whakaoti te whārite x=\frac{3±3}{-4} ina he tango te ±. Tango 3 mai i 3.

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

Whakawehe 0 ki te -4.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-\frac{3}{2} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 3x mai i ngā taha e rua.

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

Whakawehea ngā taha e rua ki te -2.

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

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

$$x^{2}+\left(-\frac{3}{-2}\right)x=\frac{0}{-2}$$

Whakawehe -3 ki te -2.

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

Whakawehe 0 ki te -2.

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

Whakawehea te \frac{3}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{4}. Nā, tāpiria te pūrua o te \frac{3}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia \frac{3}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{3}{2}x+\frac{9}{16}=\frac{9}{16}$$

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

$$\left(x+\frac{3}{4}\right)^{2}=\frac{9}{16}$$

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

$$\sqrt{\left(x+\frac{3}{4}\right)^{2}}=\sqrt{\frac{9}{16}}$$

Whakarūnātia.

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

Me tango \frac{3}{4} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{3}{2}$$