Whakaoti i te x^2+12x=13

$$x ^ { 2 } + 12 x = 13$$

Whakaoti mō x

$$x=-13$$

$$x=1$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 13 mai i ngā taha e rua.

$$x^{2}+12x-13=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}+12x-13 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.

$$a+b=12 ab=-13$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=13$$

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

$$\left(x-1\right)\left(x+13\right)$$

Hei kimi otinga whārite, me whakaoti te x-1=0 me te x+13=0.

$$x=1 x=-13$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 13 mai i ngā taha e rua.

$$x^{2}+12x-13=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx-13. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=12 ab=1\left(-13\right)=-13$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=13$$

Tuhia anō te x^{2}+12x-13 hei \left(x^{2}-x\right)+\left(13x-13\right).

$$\left(x^{2}-x\right)+\left(13x-13\right)$$

Tauwehea te x i te tuatahi me te 13 i te rōpū tuarua.

$$x\left(x-1\right)+13\left(x-1\right)$$

Whakatauwehea atu te kīanga pātahi x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-1\right)\left(x+13\right)$$

Hei kimi otinga whārite, me whakaoti te x-1=0 me te x+13=0.

$$x=1 x=-13$$

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.

$$x^{2}+12x=13$$

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

$$x^{2}+12x-13=13-13$$

Mā te tango i te 13 i a ia ake anō ka toe ko te 0.

$$x^{2}+12x-13=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 12 mō b, me -13 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-13\right)}}{2}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\left(-13\right)}}{2}$$

Whakareatia -4 ki te -13.

$$x=\frac{-12±\sqrt{144+52}}{2}$$

Tāpiri 144 ki te 52.

$$x=\frac{-12±\sqrt{196}}{2}$$

Tuhia te pūtakerua o te 196.

$$x=\frac{-12±14}{2}$$

Nā, me whakaoti te whārite x=\frac{-12±14}{2} ina he tāpiri te ±. Tāpiri -12 ki te 14.

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

Whakawehe 2 ki te 2.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{-12±14}{2} ina he tango te ±. Tango 14 mai i -12.

$$x=-\frac{26}{2}$$

Whakawehe -26 ki te 2.

$$x=-13$$

Kua oti te whārite te whakatau.

$$x=1 x=-13$$

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.

$$x^{2}+12x=13$$

Whakawehea te 12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 6. Nā, tāpiria te pūrua o te 6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+12x+6^{2}=13+6^{2}$$

Pūrua 6.

$$x^{2}+12x+36=13+36$$

Tāpiri 13 ki te 36.

$$x^{2}+12x+36=49$$

Tauwehea x^{2}+12x+36. 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}.

$$\left(x+6\right)^{2}=49$$

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

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{49}$$

Whakarūnātia.

$$x+6=7 x+6=-7$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$x=1 x=-13$$