Whakaoti i te 36m=(6-2m)(4m+3)

$$36 m = ( 6 - 2 m ) ( 4 m + 3 )$$

Whakaoti mō m

$$m=-3$$

$$m=\frac{3}{4}=0.75$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 6-2m ki te 4m+3 ka whakakotahi i ngā kupu rite.

$$36m=18m+18-8m^{2}$$

Tangohia te 18m mai i ngā taha e rua.

$$36m-18m=18-8m^{2}$$

Pahekotia te 36m me -18m, ka 18m.

$$18m=18-8m^{2}$$

Tangohia te 18 mai i ngā taha e rua.

$$18m-18=-8m^{2}$$

Me tāpiri te 8m^{2} ki ngā taha e rua.

$$18m-18+8m^{2}=0$$

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.

$$8m^{2}+18m-18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, 18 mō b, me -18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-18±\sqrt{18^{2}-4\times 8\left(-18\right)}}{2\times 8}$$

Pūrua 18.

$$m=\frac{-18±\sqrt{324-4\times 8\left(-18\right)}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$m=\frac{-18±\sqrt{324-32\left(-18\right)}}{2\times 8}$$

Whakareatia -32 ki te -18.

$$m=\frac{-18±\sqrt{324+576}}{2\times 8}$$

Tāpiri 324 ki te 576.

$$m=\frac{-18±\sqrt{900}}{2\times 8}$$

Tuhia te pūtakerua o te 900.

$$m=\frac{-18±30}{2\times 8}$$

Whakareatia 2 ki te 8.

$$m=\frac{-18±30}{16}$$

Nā, me whakaoti te whārite m=\frac{-18±30}{16} ina he tāpiri te ±. Tāpiri -18 ki te 30.

$$m=\frac{12}{16}$$

Whakahekea te hautanga \frac{12}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$m=\frac{3}{4}$$

Nā, me whakaoti te whārite m=\frac{-18±30}{16} ina he tango te ±. Tango 30 mai i -18.

$$m=-\frac{48}{16}$$

Whakawehe -48 ki te 16.

$$m=-3$$

Kua oti te whārite te whakatau.

$$m=\frac{3}{4} m=-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 6-2m ki te 4m+3 ka whakakotahi i ngā kupu rite.

$$36m=18m+18-8m^{2}$$

Tangohia te 18m mai i ngā taha e rua.

$$36m-18m=18-8m^{2}$$

Pahekotia te 36m me -18m, ka 18m.

$$18m=18-8m^{2}$$

Me tāpiri te 8m^{2} ki ngā taha e rua.

$$18m+8m^{2}=18$$

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.

$$8m^{2}+18m=18$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8m^{2}+18m}{8}=\frac{18}{8}$$

Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.

$$m^{2}+\frac{18}{8}m=\frac{18}{8}$$

Whakahekea te hautanga \frac{18}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$m^{2}+\frac{9}{4}m=\frac{18}{8}$$

Whakahekea te hautanga \frac{18}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$m^{2}+\frac{9}{4}m=\frac{9}{4}$$

Whakawehea te \frac{9}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{9}{8}. Nā, tāpiria te pūrua o te \frac{9}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$m^{2}+\frac{9}{4}m+\left(\frac{9}{8}\right)^{2}=\frac{9}{4}+\left(\frac{9}{8}\right)^{2}$$

Pūruatia \frac{9}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$m^{2}+\frac{9}{4}m+\frac{81}{64}=\frac{9}{4}+\frac{81}{64}$$

Tāpiri \frac{9}{4} ki te \frac{81}{64} 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.

$$m^{2}+\frac{9}{4}m+\frac{81}{64}=\frac{225}{64}$$

Tauwehea m^{2}+\frac{9}{4}m+\frac{81}{64}. 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}.

$$\left(m+\frac{9}{8}\right)^{2}=\frac{225}{64}$$

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

$$\sqrt{\left(m+\frac{9}{8}\right)^{2}}=\sqrt{\frac{225}{64}}$$

Whakarūnātia.

$$m+\frac{9}{8}=\frac{15}{8} m+\frac{9}{8}=-\frac{15}{8}$$

Me tango \frac{9}{8} mai i ngā taha e rua o te whārite.

$$m=\frac{3}{4} m=-3$$