Whakaoti i te m^2-6m-25=0

$$m ^ { 2 } - 6 m - 25 = 0$$

Whakaoti mō m

$$m=\sqrt{34}+3\approx 8.830951895$$

$$m=3-\sqrt{34}\approx -2.830951895$$

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.

$$m^{2}-6m-25=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -6 mō b, me -25 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua -6.

$$m=\frac{-\left(-6\right)±\sqrt{36-4\left(-25\right)}}{2}$$

Whakareatia -4 ki te -25.

$$m=\frac{-\left(-6\right)±\sqrt{36+100}}{2}$$

Tāpiri 36 ki te 100.

$$m=\frac{-\left(-6\right)±\sqrt{136}}{2}$$

Tuhia te pūtakerua o te 136.

$$m=\frac{-\left(-6\right)±2\sqrt{34}}{2}$$

Ko te tauaro o -6 ko 6.

$$m=\frac{6±2\sqrt{34}}{2}$$

Nā, me whakaoti te whārite m=\frac{6±2\sqrt{34}}{2} ina he tāpiri te ±. Tāpiri 6 ki te 2\sqrt{34}.

$$m=\frac{2\sqrt{34}+6}{2}$$

Whakawehe 6+2\sqrt{34} ki te 2.

$$m=\sqrt{34}+3$$

Nā, me whakaoti te whārite m=\frac{6±2\sqrt{34}}{2} ina he tango te ±. Tango 2\sqrt{34} mai i 6.

$$m=\frac{6-2\sqrt{34}}{2}$$

Whakawehe 6-2\sqrt{34} ki te 2.

$$m=3-\sqrt{34}$$

Kua oti te whārite te whakatau.

$$m=\sqrt{34}+3 m=3-\sqrt{34}$$

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.

$$m^{2}-6m-25=0$$

Me tāpiri 25 ki ngā taha e rua o te whārite.

$$m^{2}-6m-25-\left(-25\right)=-\left(-25\right)$$

Mā te tango i te -25 i a ia ake anō ka toe ko te 0.

$$m^{2}-6m=-\left(-25\right)$$

Tango -25 mai i 0.

$$m^{2}-6m=25$$

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

$$m^{2}-6m+\left(-3\right)^{2}=25+\left(-3\right)^{2}$$

Pūrua -3.

$$m^{2}-6m+9=25+9$$

Tāpiri 25 ki te 9.

$$m^{2}-6m+9=34$$

Tauwehea m^{2}-6m+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}.

$$\left(m-3\right)^{2}=34$$

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

$$\sqrt{\left(m-3\right)^{2}}=\sqrt{34}$$

Whakarūnātia.

$$m-3=\sqrt{34} m-3=-\sqrt{34}$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$m=\sqrt{34}+3 m=3-\sqrt{34}$$