Whakaoti i te 0.1x^2+0.3x=0

$$0.1 { x }^{ 2 } +0.3x=0$$

Whakaoti mō x

$$x=-3$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(0.1x+0.3\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te \frac{x+3}{10}=0.

$$x=0 x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$0.1x^{2}+0.3x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 0.1 mō a, 0.3 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.3±\sqrt{0.3^{2}}}{2\times 0.1}$$

Tuhia te pūtakerua o te 0.3^{2}.

$$x=\frac{-0.3±\frac{3}{10}}{2\times 0.1}$$

Whakareatia 2 ki te 0.1.

$$x=\frac{-0.3±\frac{3}{10}}{0.2}$$

Nā, me whakaoti te whārite x=\frac{-0.3±\frac{3}{10}}{0.2} ina he tāpiri te ±. Tāpiri -0.3 ki te \frac{3}{10} 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.

$$x=\frac{0}{0.2}$$

Whakawehe 0 ki te 0.2 mā te whakarea 0 ki te tau huripoki o 0.2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-0.3±\frac{3}{10}}{0.2} ina he tango te ±. Tango \frac{3}{10} mai i -0.3 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.

$$x=-\frac{\frac{3}{5}}{0.2}$$

Whakawehe -\frac{3}{5} ki te 0.2 mā te whakarea -\frac{3}{5} ki te tau huripoki o 0.2.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=0 x=-3$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$0.1x^{2}+0.3x=0$$

Me whakarea ngā taha e rua ki te 10.

$$\frac{0.1x^{2}+0.3x}{0.1}=\frac{0}{0.1}$$

Mā te whakawehe ki te 0.1 ka wetekia te whakareanga ki te 0.1.

$$x^{2}+\frac{0.3}{0.1}x=\frac{0}{0.1}$$

Whakawehe 0.3 ki te 0.1 mā te whakarea 0.3 ki te tau huripoki o 0.1.

$$x^{2}+3x=\frac{0}{0.1}$$

Whakawehe 0 ki te 0.1 mā te whakarea 0 ki te tau huripoki o 0.1.

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

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.

$$x=0 x=-3$$