Whakaoti i te k^2=-2k+35

$$k ^ { 2 } = - 2 k + 35$$

Whakaoti mō k

$$k=-7$$

$$k=5$$

Ngā Upane Whakamahi Tauwehe

Me tāpiri te 2k ki ngā taha e rua.

$$k^{2}+2k=35$$

Tangohia te 35 mai i ngā taha e rua.

$$k^{2}+2k-35=0$$

Hei whakaoti i te whārite, whakatauwehea te k^{2}+2k-35 mā te whakamahi i te tātai k^{2}+\left(a+b\right)k+ab=\left(k+a\right)\left(k+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=-35$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -35.

$$-1,35 -5,7$$

Tātaihia te tapeke mō ia takirua.

$$-1+35=34 -5+7=2$$

Ko te otinga te takirua ka hoatu i te tapeke 2.

$$a=-5 b=7$$

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

$$\left(k-5\right)\left(k+7\right)$$

Hei kimi otinga whārite, me whakaoti te k-5=0 me te k+7=0.

$$k=5 k=-7$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Me tāpiri te 2k ki ngā taha e rua.

$$k^{2}+2k=35$$

Tangohia te 35 mai i ngā taha e rua.

$$k^{2}+2k-35=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei k^{2}+ak+bk-35. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=1\left(-35\right)=-35$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -35.

$$-1,35 -5,7$$

Tātaihia te tapeke mō ia takirua.

$$-1+35=34 -5+7=2$$

Ko te otinga te takirua ka hoatu i te tapeke 2.

$$a=-5 b=7$$

Tuhia anō te k^{2}+2k-35 hei \left(k^{2}-5k\right)+\left(7k-35\right).

$$\left(k^{2}-5k\right)+\left(7k-35\right)$$

Tauwehea te k i te tuatahi me te 7 i te rōpū tuarua.

$$k\left(k-5\right)+7\left(k-5\right)$$

Whakatauwehea atu te kīanga pātahi k-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(k-5\right)\left(k+7\right)$$

Hei kimi otinga whārite, me whakaoti te k-5=0 me te k+7=0.

$$k=5 k=-7$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 2k ki ngā taha e rua.

$$k^{2}+2k=35$$

Tangohia te 35 mai i ngā taha e rua.

$$k^{2}+2k-35=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me -35 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{-2±\sqrt{2^{2}-4\left(-35\right)}}{2}$$

Pūrua 2.

$$k=\frac{-2±\sqrt{4-4\left(-35\right)}}{2}$$

Whakareatia -4 ki te -35.

$$k=\frac{-2±\sqrt{4+140}}{2}$$

Tāpiri 4 ki te 140.

$$k=\frac{-2±\sqrt{144}}{2}$$

Tuhia te pūtakerua o te 144.

$$k=\frac{-2±12}{2}$$

Nā, me whakaoti te whārite k=\frac{-2±12}{2} ina he tāpiri te ±. Tāpiri -2 ki te 12.

$$k=\frac{10}{2}$$

Whakawehe 10 ki te 2.

$$k=5$$

Nā, me whakaoti te whārite k=\frac{-2±12}{2} ina he tango te ±. Tango 12 mai i -2.

$$k=-\frac{14}{2}$$

Whakawehe -14 ki te 2.

$$k=-7$$

Kua oti te whārite te whakatau.

$$k=5 k=-7$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 2k ki ngā taha e rua.

$$k^{2}+2k=35$$

Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$k^{2}+2k+1^{2}=35+1^{2}$$

Pūrua 1.

$$k^{2}+2k+1=35+1$$

Tāpiri 35 ki te 1.

$$k^{2}+2k+1=36$$

Tauwehea k^{2}+2k+1. 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}.

$$\left(k+1\right)^{2}=36$$

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

$$\sqrt{\left(k+1\right)^{2}}=\sqrt{36}$$

Whakarūnātia.

$$k+1=6 k+1=-6$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$k=5 k=-7$$