Whakaoti i te -m^2+2m+3=3(3-m)

$$- m ^ { 2 } + 2 m + 3 = 3 ( 3 - m )$$

Whakaoti mō m

$$m=2$$

$$m=3$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 3-m.

$$-m^{2}+2m+3=9-3m$$

Tangohia te 9 mai i ngā taha e rua.

$$-m^{2}+2m+3-9=-3m$$

Tangohia te 9 i te 3, ka -6.

$$-m^{2}+2m-6=-3m$$

Me tāpiri te 3m ki ngā taha e rua.

$$-m^{2}+2m-6+3m=0$$

Pahekotia te 2m me 3m, ka 5m.

$$-m^{2}+5m-6=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -m^{2}+am+bm-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=-\left(-6\right)=6$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 6.

$$1,6 2,3$$

Tātaihia te tapeke mō ia takirua.

$$1+6=7 2+3=5$$

Ko te otinga te takirua ka hoatu i te tapeke 5.

$$a=3 b=2$$

Tuhia anō te -m^{2}+5m-6 hei \left(-m^{2}+3m\right)+\left(2m-6\right).

$$\left(-m^{2}+3m\right)+\left(2m-6\right)$$

Tauwehea te -m i te tuatahi me te 2 i te rōpū tuarua.

$$-m\left(m-3\right)+2\left(m-3\right)$$

Whakatauwehea atu te kīanga pātahi m-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(m-3\right)\left(-m+2\right)$$

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

$$m=3 m=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 3-m.

$$-m^{2}+2m+3=9-3m$$

Tangohia te 9 mai i ngā taha e rua.

$$-m^{2}+2m+3-9=-3m$$

Tangohia te 9 i te 3, ka -6.

$$-m^{2}+2m-6=-3m$$

Me tāpiri te 3m ki ngā taha e rua.

$$-m^{2}+2m-6+3m=0$$

Pahekotia te 2m me 3m, ka 5m.

$$-m^{2}+5m-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 5 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-5±\sqrt{5^{2}-4\left(-1\right)\left(-6\right)}}{2\left(-1\right)}$$

Pūrua 5.

$$m=\frac{-5±\sqrt{25-4\left(-1\right)\left(-6\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$m=\frac{-5±\sqrt{25+4\left(-6\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -6.

$$m=\frac{-5±\sqrt{25-24}}{2\left(-1\right)}$$

Tāpiri 25 ki te -24.

$$m=\frac{-5±\sqrt{1}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 1.

$$m=\frac{-5±1}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$m=\frac{-5±1}{-2}$$

Nā, me whakaoti te whārite m=\frac{-5±1}{-2} ina he tāpiri te ±. Tāpiri -5 ki te 1.

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

Whakawehe -4 ki te -2.

$$m=2$$

Nā, me whakaoti te whārite m=\frac{-5±1}{-2} ina he tango te ±. Tango 1 mai i -5.

$$m=-\frac{6}{-2}$$

Whakawehe -6 ki te -2.

$$m=3$$

Kua oti te whārite te whakatau.

$$m=2 m=3$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 3-m.

$$-m^{2}+2m+3=9-3m$$

Me tāpiri te 3m ki ngā taha e rua.

$$-m^{2}+2m+3+3m=9$$

Pahekotia te 2m me 3m, ka 5m.

$$-m^{2}+5m+3=9$$

Tangohia te 3 mai i ngā taha e rua.

$$-m^{2}+5m=9-3$$

Tangohia te 3 i te 9, ka 6.

$$-m^{2}+5m=6$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-m^{2}+5m}{-1}=\frac{6}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$m^{2}+\frac{5}{-1}m=\frac{6}{-1}$$

Whakawehe 5 ki te -1.

$$m^{2}-5m=\frac{6}{-1}$$

Whakawehe 6 ki te -1.

$$m^{2}-5m=-6$$

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

$$m^{2}-5m+\left(-\frac{5}{2}\right)^{2}=-6+\left(-\frac{5}{2}\right)^{2}$$

Pūruatia -\frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$m^{2}-5m+\frac{25}{4}=-6+\frac{25}{4}$$

Tāpiri -6 ki te \frac{25}{4}.

$$m^{2}-5m+\frac{25}{4}=\frac{1}{4}$$

Tauwehea m^{2}-5m+\frac{25}{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}.

$$\left(m-\frac{5}{2}\right)^{2}=\frac{1}{4}$$

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

$$\sqrt{\left(m-\frac{5}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Whakarūnātia.

$$m-\frac{5}{2}=\frac{1}{2} m-\frac{5}{2}=-\frac{1}{2}$$

Me tāpiri \frac{5}{2} ki ngā taha e rua o te whārite.

$$m=3 m=2$$