Whakaoti i te 3x+2/6*x+2/3=0

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

Whakaoti mō x

$$x=-2$$

$$x=-\frac{2}{3}\approx -0.666666667$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 6,3.

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

Tuhia te \left(3x+2\right)\times \frac{x+2}{3} hei hautanga kotahi.

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

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 3x+2 ki ia tau o x+2.

$$\frac{3x^{2}+6x+2x+4}{3}=0$$

Pahekotia te 6x me 2x, ka 8x.

$$\frac{3x^{2}+8x+4}{3}=0$$

Whakawehea ia wā o 3x^{2}+8x+4 ki te 3, kia riro ko x^{2}+\frac{8}{3}x+\frac{4}{3}.

$$x^{2}+\frac{8}{3}x+\frac{4}{3}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, \frac{8}{3} mō b, me \frac{4}{3} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{8}{3}±\sqrt{\left(\frac{8}{3}\right)^{2}-4\times \frac{4}{3}}}{2}$$

Pūruatia \frac{8}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\frac{8}{3}±\sqrt{\frac{64}{9}-4\times \frac{4}{3}}}{2}$$

Whakareatia -4 ki te \frac{4}{3}.

$$x=\frac{-\frac{8}{3}±\sqrt{\frac{64}{9}-\frac{16}{3}}}{2}$$

Tāpiri \frac{64}{9} ki te -\frac{16}{3} 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.

$$x=\frac{-\frac{8}{3}±\sqrt{\frac{16}{9}}}{2}$$

Tuhia te pūtakerua o te \frac{16}{9}.

$$x=\frac{-\frac{8}{3}±\frac{4}{3}}{2}$$

Nā, me whakaoti te whārite x=\frac{-\frac{8}{3}±\frac{4}{3}}{2} ina he tāpiri te ±. Tāpiri -\frac{8}{3} ki te \frac{4}{3} 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.

$$x=-\frac{\frac{4}{3}}{2}$$

Whakawehe -\frac{4}{3} ki te 2.

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

Nā, me whakaoti te whārite x=\frac{-\frac{8}{3}±\frac{4}{3}}{2} ina he tango te ±. Tango \frac{4}{3} mai i -\frac{8}{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.

$$x=-\frac{4}{2}$$

Whakawehe -4 ki te 2.

$$x=-2$$

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 6,3.

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

Tuhia te \left(3x+2\right)\times \frac{x+2}{3} hei hautanga kotahi.

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

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 3x+2 ki ia tau o x+2.

$$\frac{3x^{2}+6x+2x+4}{3}=0$$

Pahekotia te 6x me 2x, ka 8x.

$$\frac{3x^{2}+8x+4}{3}=0$$

Whakawehea ia wā o 3x^{2}+8x+4 ki te 3, kia riro ko x^{2}+\frac{8}{3}x+\frac{4}{3}.

$$x^{2}+\frac{8}{3}x+\frac{4}{3}=0$$

Tangohia te \frac{4}{3} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}+\frac{8}{3}x=-\frac{4}{3}$$

Whakawehea te \frac{8}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{4}{3}. Nā, tāpiria te pūrua o te \frac{4}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{8}{3}x+\left(\frac{4}{3}\right)^{2}=-\frac{4}{3}+\left(\frac{4}{3}\right)^{2}$$

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

$$x^{2}+\frac{8}{3}x+\frac{16}{9}=-\frac{4}{3}+\frac{16}{9}$$

Tāpiri -\frac{4}{3} ki te \frac{16}{9} 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.

$$x^{2}+\frac{8}{3}x+\frac{16}{9}=\frac{4}{9}$$

Tauwehea x^{2}+\frac{8}{3}x+\frac{16}{9}. 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}.

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

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

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

Whakarūnātia.

$$x+\frac{4}{3}=\frac{2}{3} x+\frac{4}{3}=-\frac{2}{3}$$

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

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