Whakaoti i te s^2-5s-50=0

$$s ^ { 2 } - 5 s - 50 = 0$$

Whakaoti mō s

$$s=-5$$

$$s=10$$

Ngā Upane Whakamahi Tauwehe

Hei whakaoti i te whārite, whakatauwehea te s^{2}-5s-50 mā te whakamahi i te tātai s^{2}+\left(a+b\right)s+ab=\left(s+a\right)\left(s+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-5 ab=-50$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -50.

$$1,-50 2,-25 5,-10$$

Tātaihia te tapeke mō ia takirua.

$$1-50=-49 2-25=-23 5-10=-5$$

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

$$a=-10 b=5$$

Me tuhi anō te kīanga whakatauwehe \left(s+a\right)\left(s+b\right) mā ngā uara i tātaihia.

$$\left(s-10\right)\left(s+5\right)$$

Hei kimi otinga whārite, me whakaoti te s-10=0 me te s+5=0.

$$s=10 s=-5$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei s^{2}+as+bs-50. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-5 ab=1\left(-50\right)=-50$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -50.

$$1,-50 2,-25 5,-10$$

Tātaihia te tapeke mō ia takirua.

$$1-50=-49 2-25=-23 5-10=-5$$

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

$$a=-10 b=5$$

Tuhia anō te s^{2}-5s-50 hei \left(s^{2}-10s\right)+\left(5s-50\right).

$$\left(s^{2}-10s\right)+\left(5s-50\right)$$

Tauwehea te s i te tuatahi me te 5 i te rōpū tuarua.

$$s\left(s-10\right)+5\left(s-10\right)$$

Whakatauwehea atu te kīanga pātahi s-10 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(s-10\right)\left(s+5\right)$$

Hei kimi otinga whārite, me whakaoti te s-10=0 me te s+5=0.

$$s=10 s=-5$$

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.

$$s^{2}-5s-50=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -5 mō b, me -50 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-50\right)}}{2}$$

Pūrua -5.

$$s=\frac{-\left(-5\right)±\sqrt{25-4\left(-50\right)}}{2}$$

Whakareatia -4 ki te -50.

$$s=\frac{-\left(-5\right)±\sqrt{25+200}}{2}$$

Tāpiri 25 ki te 200.

$$s=\frac{-\left(-5\right)±\sqrt{225}}{2}$$

Tuhia te pūtakerua o te 225.

$$s=\frac{-\left(-5\right)±15}{2}$$

Ko te tauaro o -5 ko 5.

$$s=\frac{5±15}{2}$$

Nā, me whakaoti te whārite s=\frac{5±15}{2} ina he tāpiri te ±. Tāpiri 5 ki te 15.

$$s=\frac{20}{2}$$

Whakawehe 20 ki te 2.

$$s=10$$

Nā, me whakaoti te whārite s=\frac{5±15}{2} ina he tango te ±. Tango 15 mai i 5.

$$s=-\frac{10}{2}$$

Whakawehe -10 ki te 2.

$$s=-5$$

Kua oti te whārite te whakatau.

$$s=10 s=-5$$

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.

$$s^{2}-5s-50=0$$

Me tāpiri 50 ki ngā taha e rua o te whārite.

$$s^{2}-5s-50-\left(-50\right)=-\left(-50\right)$$

Mā te tango i te -50 i a ia ake anō ka toe ko te 0.

$$s^{2}-5s=-\left(-50\right)$$

Tango -50 mai i 0.

$$s^{2}-5s=50$$

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.

$$s^{2}-5s+\left(-\frac{5}{2}\right)^{2}=50+\left(-\frac{5}{2}\right)^{2}$$

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

$$s^{2}-5s+\frac{25}{4}=50+\frac{25}{4}$$

Tāpiri 50 ki te \frac{25}{4}.

$$s^{2}-5s+\frac{25}{4}=\frac{225}{4}$$

Tauwehea s^{2}-5s+\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}.

$$\left(s-\frac{5}{2}\right)^{2}=\frac{225}{4}$$

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

$$\sqrt{\left(s-\frac{5}{2}\right)^{2}}=\sqrt{\frac{225}{4}}$$

Whakarūnātia.

$$s-\frac{5}{2}=\frac{15}{2} s-\frac{5}{2}=-\frac{15}{2}$$

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

$$s=10 s=-5$$