Whakaoti i te m^2+6m+13+m^2+16=45

$$m ^ { 2 } + 6 m + 13 + m ^ { 2 } + 16 = 45$$

Whakaoti mō m

$$m = \frac{\sqrt{41} - 3}{2} \approx 1.701562119$$

$$m=\frac{-\sqrt{41}-3}{2}\approx -4.701562119$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te m^{2} me m^{2}, ka 2m^{2}.

$$2m^{2}+6m+13+16=45$$

Tāpirihia te 13 ki te 16, ka 29.

$$2m^{2}+6m+29=45$$

Tangohia te 45 mai i ngā taha e rua.

$$2m^{2}+6m+29-45=0$$

Tangohia te 45 i te 29, ka -16.

$$2m^{2}+6m-16=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 6 mō b, me -16 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-6±\sqrt{6^{2}-4\times 2\left(-16\right)}}{2\times 2}$$

Pūrua 6.

$$m=\frac{-6±\sqrt{36-4\times 2\left(-16\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$m=\frac{-6±\sqrt{36-8\left(-16\right)}}{2\times 2}$$

Whakareatia -8 ki te -16.

$$m=\frac{-6±\sqrt{36+128}}{2\times 2}$$

Tāpiri 36 ki te 128.

$$m=\frac{-6±\sqrt{164}}{2\times 2}$$

Tuhia te pūtakerua o te 164.

$$m=\frac{-6±2\sqrt{41}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$m=\frac{-6±2\sqrt{41}}{4}$$

Nā, me whakaoti te whārite m=\frac{-6±2\sqrt{41}}{4} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{41}.

$$m=\frac{2\sqrt{41}-6}{4}$$

Whakawehe -6+2\sqrt{41} ki te 4.

$$m=\frac{\sqrt{41}-3}{2}$$

Nā, me whakaoti te whārite m=\frac{-6±2\sqrt{41}}{4} ina he tango te ±. Tango 2\sqrt{41} mai i -6.

$$m=\frac{-2\sqrt{41}-6}{4}$$

Whakawehe -6-2\sqrt{41} ki te 4.

$$m=\frac{-\sqrt{41}-3}{2}$$

Kua oti te whārite te whakatau.

$$m=\frac{\sqrt{41}-3}{2} m=\frac{-\sqrt{41}-3}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te m^{2} me m^{2}, ka 2m^{2}.

$$2m^{2}+6m+13+16=45$$

Tāpirihia te 13 ki te 16, ka 29.

$$2m^{2}+6m+29=45$$

Tangohia te 29 mai i ngā taha e rua.

$$2m^{2}+6m=45-29$$

Tangohia te 29 i te 45, ka 16.

$$2m^{2}+6m=16$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2m^{2}+6m}{2}=\frac{16}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$m^{2}+\frac{6}{2}m=\frac{16}{2}$$

Whakawehe 6 ki te 2.

$$m^{2}+3m=\frac{16}{2}$$

Whakawehe 16 ki te 2.

$$m^{2}+3m=8$$

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.

$$m^{2}+3m+\left(\frac{3}{2}\right)^{2}=8+\left(\frac{3}{2}\right)^{2}$$

Pūruatia \frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

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

Tāpiri 8 ki te \frac{9}{4}.

$$m^{2}+3m+\frac{9}{4}=\frac{41}{4}$$

Tauwehea m^{2}+3m+\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}.

$$\left(m+\frac{3}{2}\right)^{2}=\frac{41}{4}$$

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

$$\sqrt{\left(m+\frac{3}{2}\right)^{2}}=\sqrt{\frac{41}{4}}$$

Whakarūnātia.

$$m+\frac{3}{2}=\frac{\sqrt{41}}{2} m+\frac{3}{2}=-\frac{\sqrt{41}}{2}$$

Me tango \frac{3}{2} mai i ngā taha e rua o te whārite.

$$m=\frac{\sqrt{41}-3}{2} m=\frac{-\sqrt{41}-3}{2}$$