Whakaoti i te m^2+26m-15=0

$$m ^ { 2 } + 26 m - 15 = 0$$

Whakaoti mō m

$$m=2\sqrt{46}-13\approx 0.564659966$$

$$m=-2\sqrt{46}-13\approx -26.564659966$$

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.

$$m^{2}+26m-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 26 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-26±\sqrt{26^{2}-4\left(-15\right)}}{2}$$

Pūrua 26.

$$m=\frac{-26±\sqrt{676-4\left(-15\right)}}{2}$$

Whakareatia -4 ki te -15.

$$m=\frac{-26±\sqrt{676+60}}{2}$$

Tāpiri 676 ki te 60.

$$m=\frac{-26±\sqrt{736}}{2}$$

Tuhia te pūtakerua o te 736.

$$m=\frac{-26±4\sqrt{46}}{2}$$

Nā, me whakaoti te whārite m=\frac{-26±4\sqrt{46}}{2} ina he tāpiri te ±. Tāpiri -26 ki te 4\sqrt{46}.

$$m=\frac{4\sqrt{46}-26}{2}$$

Whakawehe -26+4\sqrt{46} ki te 2.

$$m=2\sqrt{46}-13$$

Nā, me whakaoti te whārite m=\frac{-26±4\sqrt{46}}{2} ina he tango te ±. Tango 4\sqrt{46} mai i -26.

$$m=\frac{-4\sqrt{46}-26}{2}$$

Whakawehe -26-4\sqrt{46} ki te 2.

$$m=-2\sqrt{46}-13$$

Kua oti te whārite te whakatau.

$$m=2\sqrt{46}-13 m=-2\sqrt{46}-13$$

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.

$$m^{2}+26m-15=0$$

Me tāpiri 15 ki ngā taha e rua o te whārite.

$$m^{2}+26m-15-\left(-15\right)=-\left(-15\right)$$

Mā te tango i te -15 i a ia ake anō ka toe ko te 0.

$$m^{2}+26m=-\left(-15\right)$$

Tango -15 mai i 0.

$$m^{2}+26m=15$$

Whakawehea te 26, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 13. Nā, tāpiria te pūrua o te 13 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$m^{2}+26m+13^{2}=15+13^{2}$$

Pūrua 13.

$$m^{2}+26m+169=15+169$$

Tāpiri 15 ki te 169.

$$m^{2}+26m+169=184$$

Tauwehea m^{2}+26m+169. 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}.

$$\left(m+13\right)^{2}=184$$

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

$$\sqrt{\left(m+13\right)^{2}}=\sqrt{184}$$

Whakarūnātia.

$$m+13=2\sqrt{46} m+13=-2\sqrt{46}$$

Me tango 13 mai i ngā taha e rua o te whārite.

$$m=2\sqrt{46}-13 m=-2\sqrt{46}-13$$