Whakaoti i te 64=49+c^2-2*7c(-1/7)

$$64 = 49+ { c }^{ 2 } -2 \cdot 7c(- \frac{ 1 }{ 7 } )$$

Whakaoti mō c

$$c=-5$$

$$c=3$$

Ngā Upane Whakamahi Tauwehe

Whakareatia te 2 ki te 7, ka 14.

$$64=49+c^{2}-14c\left(-\frac{1}{7}\right)$$

Whakareatia te 14 ki te -\frac{1}{7}, ka -2.

$$64=49+c^{2}-\left(-2c\right)$$

Ko te tauaro o -2c ko 2c.

$$64=49+c^{2}+2c$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$49+c^{2}+2c=64$$

Tangohia te 64 mai i ngā taha e rua.

$$49+c^{2}+2c-64=0$$

Tangohia te 64 i te 49, ka -15.

$$-15+c^{2}+2c=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$c^{2}+2c-15=0$$

Hei whakaoti i te whārite, whakatauwehea te c^{2}+2c-15 mā te whakamahi i te tātai c^{2}+\left(a+b\right)c+ab=\left(c+a\right)\left(c+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=-15$$

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 -15.

$$-1,15 -3,5$$

Tātaihia te tapeke mō ia takirua.

$$-1+15=14 -3+5=2$$

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

$$a=-3 b=5$$

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

$$\left(c-3\right)\left(c+5\right)$$

Hei kimi otinga whārite, me whakaoti te c-3=0 me te c+5=0.

$$c=3 c=-5$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakareatia te 2 ki te 7, ka 14.

$$64=49+c^{2}-14c\left(-\frac{1}{7}\right)$$

Whakareatia te 14 ki te -\frac{1}{7}, ka -2.

$$64=49+c^{2}-\left(-2c\right)$$

Ko te tauaro o -2c ko 2c.

$$64=49+c^{2}+2c$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$49+c^{2}+2c=64$$

Tangohia te 64 mai i ngā taha e rua.

$$49+c^{2}+2c-64=0$$

Tangohia te 64 i te 49, ka -15.

$$-15+c^{2}+2c=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$c^{2}+2c-15=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei c^{2}+ac+bc-15. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=1\left(-15\right)=-15$$

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 -15.

$$-1,15 -3,5$$

Tātaihia te tapeke mō ia takirua.

$$-1+15=14 -3+5=2$$

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

$$a=-3 b=5$$

Tuhia anō te c^{2}+2c-15 hei \left(c^{2}-3c\right)+\left(5c-15\right).

$$\left(c^{2}-3c\right)+\left(5c-15\right)$$

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

$$c\left(c-3\right)+5\left(c-3\right)$$

Whakatauwehea atu te kīanga pātahi c-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(c-3\right)\left(c+5\right)$$

Hei kimi otinga whārite, me whakaoti te c-3=0 me te c+5=0.

$$c=3 c=-5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 2 ki te 7, ka 14.

$$64=49+c^{2}-14c\left(-\frac{1}{7}\right)$$

Whakareatia te 14 ki te -\frac{1}{7}, ka -2.

$$64=49+c^{2}-\left(-2c\right)$$

Ko te tauaro o -2c ko 2c.

$$64=49+c^{2}+2c$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$49+c^{2}+2c=64$$

Tangohia te 64 mai i ngā taha e rua.

$$49+c^{2}+2c-64=0$$

Tangohia te 64 i te 49, ka -15.

$$-15+c^{2}+2c=0$$

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.

$$c^{2}+2c-15=0$$

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

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

Pūrua 2.

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

Whakareatia -4 ki te -15.

$$c=\frac{-2±\sqrt{4+60}}{2}$$

Tāpiri 4 ki te 60.

$$c=\frac{-2±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$c=\frac{-2±8}{2}$$

Nā, me whakaoti te whārite c=\frac{-2±8}{2} ina he tāpiri te ±. Tāpiri -2 ki te 8.

$$c=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$c=3$$

Nā, me whakaoti te whārite c=\frac{-2±8}{2} ina he tango te ±. Tango 8 mai i -2.

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

Whakawehe -10 ki te 2.

$$c=-5$$

Kua oti te whārite te whakatau.

$$c=3 c=-5$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 2 ki te 7, ka 14.

$$64=49+c^{2}-14c\left(-\frac{1}{7}\right)$$

Whakareatia te 14 ki te -\frac{1}{7}, ka -2.

$$64=49+c^{2}-\left(-2c\right)$$

Ko te tauaro o -2c ko 2c.

$$64=49+c^{2}+2c$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$49+c^{2}+2c=64$$

Tangohia te 49 mai i ngā taha e rua.

$$c^{2}+2c=64-49$$

Tangohia te 49 i te 64, ka 15.

$$c^{2}+2c=15$$

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.

$$c^{2}+2c+1^{2}=15+1^{2}$$

Pūrua 1.

$$c^{2}+2c+1=15+1$$

Tāpiri 15 ki te 1.

$$c^{2}+2c+1=16$$

Tauwehea c^{2}+2c+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}.

$$\left(c+1\right)^{2}=16$$

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

$$\sqrt{\left(c+1\right)^{2}}=\sqrt{16}$$

Whakarūnātia.

$$c+1=4 c+1=-4$$

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

$$c=3 c=-5$$