Whakaoti i te x^2+20x-18=3

$$x ^ { 2 } + 20 x - 18 = 3$$

Whakaoti mō x

$$x=-21$$

$$x=1$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 3 mai i ngā taha e rua.

$$x^{2}+20x-18-3=0$$

Tangohia te 3 i te -18, ka -21.

$$x^{2}+20x-21=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}+20x-21 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.

$$a+b=20 ab=-21$$

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 -21.

$$-1,21 -3,7$$

Tātaihia te tapeke mō ia takirua.

$$-1+21=20 -3+7=4$$

Ko te otinga te takirua ka hoatu i te tapeke 20.

$$a=-1 b=21$$

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

$$\left(x-1\right)\left(x+21\right)$$

Hei kimi otinga whārite, me whakaoti te x-1=0 me te x+21=0.

$$x=1 x=-21$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 3 mai i ngā taha e rua.

$$x^{2}+20x-18-3=0$$

Tangohia te 3 i te -18, ka -21.

$$x^{2}+20x-21=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx-21. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=20 ab=1\left(-21\right)=-21$$

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 -21.

$$-1,21 -3,7$$

Tātaihia te tapeke mō ia takirua.

$$-1+21=20 -3+7=4$$

Ko te otinga te takirua ka hoatu i te tapeke 20.

$$a=-1 b=21$$

Tuhia anō te x^{2}+20x-21 hei \left(x^{2}-x\right)+\left(21x-21\right).

$$\left(x^{2}-x\right)+\left(21x-21\right)$$

Tauwehea te x i te tuatahi me te 21 i te rōpū tuarua.

$$x\left(x-1\right)+21\left(x-1\right)$$

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

$$\left(x-1\right)\left(x+21\right)$$

Hei kimi otinga whārite, me whakaoti te x-1=0 me te x+21=0.

$$x=1 x=-21$$

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.

$$x^{2}+20x-18=3$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$x^{2}+20x-18-3=3-3$$

Mā te tango i te 3 i a ia ake anō ka toe ko te 0.

$$x^{2}+20x-18-3=0$$

Tango 3 mai i -18.

$$x^{2}+20x-21=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 20 mō b, me -21 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-20±\sqrt{20^{2}-4\left(-21\right)}}{2}$$

Pūrua 20.

$$x=\frac{-20±\sqrt{400-4\left(-21\right)}}{2}$$

Whakareatia -4 ki te -21.

$$x=\frac{-20±\sqrt{400+84}}{2}$$

Tāpiri 400 ki te 84.

$$x=\frac{-20±\sqrt{484}}{2}$$

Tuhia te pūtakerua o te 484.

$$x=\frac{-20±22}{2}$$

Nā, me whakaoti te whārite x=\frac{-20±22}{2} ina he tāpiri te ±. Tāpiri -20 ki te 22.

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

Whakawehe 2 ki te 2.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{-20±22}{2} ina he tango te ±. Tango 22 mai i -20.

$$x=-\frac{42}{2}$$

Whakawehe -42 ki te 2.

$$x=-21$$

Kua oti te whārite te whakatau.

$$x=1 x=-21$$

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.

$$x^{2}+20x-18=3$$

Me tāpiri 18 ki ngā taha e rua o te whārite.

$$x^{2}+20x-18-\left(-18\right)=3-\left(-18\right)$$

Mā te tango i te -18 i a ia ake anō ka toe ko te 0.

$$x^{2}+20x=3-\left(-18\right)$$

Tango -18 mai i 3.

$$x^{2}+20x=21$$

Whakawehea te 20, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 10. Nā, tāpiria te pūrua o te 10 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+20x+10^{2}=21+10^{2}$$

Pūrua 10.

$$x^{2}+20x+100=21+100$$

Tāpiri 21 ki te 100.

$$x^{2}+20x+100=121$$

Tauwehea x^{2}+20x+100. 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}.

$$\left(x+10\right)^{2}=121$$

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

$$\sqrt{\left(x+10\right)^{2}}=\sqrt{121}$$

Whakarūnātia.

$$x+10=11 x+10=-11$$

Me tango 10 mai i ngā taha e rua o te whārite.

$$x=1 x=-21$$