Whakaoti i te m^2-40m-56=0

$${ m }^{ 2 } -40m-56 = 0$$

Whakaoti mō m

$$m=2\sqrt{114}+20\approx 41.354156504$$

$$m=20-2\sqrt{114}\approx -1.354156504$$

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.

$$m^{2}-40m-56=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -40 mō b, me -56 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-40\right)±\sqrt{\left(-40\right)^{2}-4\left(-56\right)}}{2}$$

Pūrua -40.

$$m=\frac{-\left(-40\right)±\sqrt{1600-4\left(-56\right)}}{2}$$

Whakareatia -4 ki te -56.

$$m=\frac{-\left(-40\right)±\sqrt{1600+224}}{2}$$

Tāpiri 1600 ki te 224.

$$m=\frac{-\left(-40\right)±\sqrt{1824}}{2}$$

Tuhia te pūtakerua o te 1824.

$$m=\frac{-\left(-40\right)±4\sqrt{114}}{2}$$

Ko te tauaro o -40 ko 40.

$$m=\frac{40±4\sqrt{114}}{2}$$

Nā, me whakaoti te whārite m=\frac{40±4\sqrt{114}}{2} ina he tāpiri te ±. Tāpiri 40 ki te 4\sqrt{114}.

$$m=\frac{4\sqrt{114}+40}{2}$$

Whakawehe 40+4\sqrt{114} ki te 2.

$$m=2\sqrt{114}+20$$

Nā, me whakaoti te whārite m=\frac{40±4\sqrt{114}}{2} ina he tango te ±. Tango 4\sqrt{114} mai i 40.

$$m=\frac{40-4\sqrt{114}}{2}$$

Whakawehe 40-4\sqrt{114} ki te 2.

$$m=20-2\sqrt{114}$$

Kua oti te whārite te whakatau.

$$m=2\sqrt{114}+20 m=20-2\sqrt{114}$$

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.

$$m^{2}-40m-56=0$$

Me tāpiri 56 ki ngā taha e rua o te whārite.

$$m^{2}-40m-56-\left(-56\right)=-\left(-56\right)$$

Mā te tango i te -56 i a ia ake anō ka toe ko te 0.

$$m^{2}-40m=-\left(-56\right)$$

Tango -56 mai i 0.

$$m^{2}-40m=56$$

Whakawehea te -40, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -20. Nā, tāpiria te pūrua o te -20 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$m^{2}-40m+\left(-20\right)^{2}=56+\left(-20\right)^{2}$$

Pūrua -20.

$$m^{2}-40m+400=56+400$$

Tāpiri 56 ki te 400.

$$m^{2}-40m+400=456$$

Tauwehea m^{2}-40m+400. 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}.

$$\left(m-20\right)^{2}=456$$

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

$$\sqrt{\left(m-20\right)^{2}}=\sqrt{456}$$

Whakarūnātia.

$$m-20=2\sqrt{114} m-20=-2\sqrt{114}$$

Me tāpiri 20 ki ngā taha e rua o te whārite.

$$m=2\sqrt{114}+20 m=20-2\sqrt{114}$$