Whakaoti i te 5/3x^2+2x=0

$$\frac { 5 } { 3 } x ^ { 2 } + 2 x = 0$$

Whakaoti mō x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(\frac{5}{3}x+2\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te \frac{5x}{3}+2=0.

$$x=0 x=-\frac{6}{5}$$

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.

$$\frac{5}{3}x^{2}+2x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{5}{3} mō a, 2 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}}}{2\times \frac{5}{3}}$$

Tuhia te pūtakerua o te 2^{2}.

$$x=\frac{-2±2}{2\times \frac{5}{3}}$$

Whakareatia 2 ki te \frac{5}{3}.

$$x=\frac{-2±2}{\frac{10}{3}}$$

Nā, me whakaoti te whārite x=\frac{-2±2}{\frac{10}{3}} ina he tāpiri te ±. Tāpiri -2 ki te 2.

$$x=\frac{0}{\frac{10}{3}}$$

Whakawehe 0 ki te \frac{10}{3} mā te whakarea 0 ki te tau huripoki o \frac{10}{3}.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-2±2}{\frac{10}{3}} ina he tango te ±. Tango 2 mai i -2.

$$x=-\frac{4}{\frac{10}{3}}$$

Whakawehe -4 ki te \frac{10}{3} mā te whakarea -4 ki te tau huripoki o \frac{10}{3}.

$$x=-\frac{6}{5}$$

Kua oti te whārite te whakatau.

$$x=0 x=-\frac{6}{5}$$

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.

$$\frac{5}{3}x^{2}+2x=0$$

Whakawehea ngā taha e rua o te whārite ki te \frac{5}{3}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{\frac{5}{3}x^{2}+2x}{\frac{5}{3}}=\frac{0}{\frac{5}{3}}$$

Mā te whakawehe ki te \frac{5}{3} ka wetekia te whakareanga ki te \frac{5}{3}.

$$x^{2}+\frac{2}{\frac{5}{3}}x=\frac{0}{\frac{5}{3}}$$

Whakawehe 2 ki te \frac{5}{3} mā te whakarea 2 ki te tau huripoki o \frac{5}{3}.

$$x^{2}+\frac{6}{5}x=\frac{0}{\frac{5}{3}}$$

Whakawehe 0 ki te \frac{5}{3} mā te whakarea 0 ki te tau huripoki o \frac{5}{3}.

$$x^{2}+\frac{6}{5}x=0$$

Whakawehea te \frac{6}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{5}. Nā, tāpiria te pūrua o te \frac{3}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{6}{5}x+\left(\frac{3}{5}\right)^{2}=\left(\frac{3}{5}\right)^{2}$$

Pūruatia \frac{3}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{6}{5}x+\frac{9}{25}=\frac{9}{25}$$

Tauwehea te x^{2}+\frac{6}{5}x+\frac{9}{25}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{3}{5}\right)^{2}=\frac{9}{25}$$

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

$$\sqrt{\left(x+\frac{3}{5}\right)^{2}}=\sqrt{\frac{9}{25}}$$

Whakarūnātia.

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

Me tango \frac{3}{5} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{6}{5}$$