Whakaoti i te x^2+2x-63=0

$$x ^ { 2 } + 2 x - 63 = 0$$

Whakaoti mō x

$$x=-9$$

$$x=7$$

Ngā Upane Whakamahi Tauwehe

Hei whakaoti i te whārite, whakatauwehea te x^{2}+2x-63 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=-63$$

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 -63.

$$-1,63 -3,21 -7,9$$

Tātaihia te tapeke mō ia takirua.

$$-1+63=62 -3+21=18 -7+9=2$$

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

$$a=-7 b=9$$

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

$$\left(x-7\right)\left(x+9\right)$$

Hei kimi otinga whārite, me whakaoti te x-7=0 me te x+9=0.

$$x=7 x=-9$$

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 x^{2}+ax+bx-63. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=1\left(-63\right)=-63$$

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 -63.

$$-1,63 -3,21 -7,9$$

Tātaihia te tapeke mō ia takirua.

$$-1+63=62 -3+21=18 -7+9=2$$

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

$$a=-7 b=9$$

Tuhia anō te x^{2}+2x-63 hei \left(x^{2}-7x\right)+\left(9x-63\right).

$$\left(x^{2}-7x\right)+\left(9x-63\right)$$

Tauwehea te x i te tuatahi me te 9 i te rōpū tuarua.

$$x\left(x-7\right)+9\left(x-7\right)$$

Whakatauwehea atu te kīanga pātahi x-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-7\right)\left(x+9\right)$$

Hei kimi otinga whārite, me whakaoti te x-7=0 me te x+9=0.

$$x=7 x=-9$$

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.

$$x^{2}+2x-63=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me -63 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-63\right)}}{2}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\left(-63\right)}}{2}$$

Whakareatia -4 ki te -63.

$$x=\frac{-2±\sqrt{4+252}}{2}$$

Tāpiri 4 ki te 252.

$$x=\frac{-2±\sqrt{256}}{2}$$

Tuhia te pūtakerua o te 256.

$$x=\frac{-2±16}{2}$$

Nā, me whakaoti te whārite x=\frac{-2±16}{2} ina he tāpiri te ±. Tāpiri -2 ki te 16.

$$x=\frac{14}{2}$$

Whakawehe 14 ki te 2.

$$x=7$$

Nā, me whakaoti te whārite x=\frac{-2±16}{2} ina he tango te ±. Tango 16 mai i -2.

$$x=-\frac{18}{2}$$

Whakawehe -18 ki te 2.

$$x=-9$$

Kua oti te whārite te whakatau.

$$x=7 x=-9$$

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.

$$x^{2}+2x-63=0$$

Me tāpiri 63 ki ngā taha e rua o te whārite.

$$x^{2}+2x-63-\left(-63\right)=-\left(-63\right)$$

Mā te tango i te -63 i a ia ake anō ka toe ko te 0.

$$x^{2}+2x=-\left(-63\right)$$

Tango -63 mai i 0.

$$x^{2}+2x=63$$

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.

$$x^{2}+2x+1^{2}=63+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=63+1$$

Tāpiri 63 ki te 1.

$$x^{2}+2x+1=64$$

Tauwehea x^{2}+2x+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}.

$$\left(x+1\right)^{2}=64$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{64}$$

Whakarūnātia.

$$x+1=8 x+1=-8$$

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

$$x=7 x=-9$$