Whakaoti i te x^2(x+6)-x(x+6)=30(x+6)

$$x ^ { 2 } ( x + 6 ) - x ( x + 6 ) = 30 ( x + 6 )$$

Whakaoti mō x

$$x=-5$$

$$x=6$$

$$x=-6$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2} ki te x+6.

$$x^{3}+6x^{2}-x\left(x+6\right)=30\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+6.

$$x^{3}+6x^{2}-\left(x^{2}+6x\right)=30\left(x+6\right)$$

Hei kimi i te tauaro o x^{2}+6x, kimihia te tauaro o ia taurangi.

$$x^{3}+6x^{2}-x^{2}-6x=30\left(x+6\right)$$

Pahekotia te 6x^{2} me -x^{2}, ka 5x^{2}.

$$x^{3}+5x^{2}-6x=30\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 30 ki te x+6.

$$x^{3}+5x^{2}-6x=30x+180$$

Tangohia te 30x mai i ngā taha e rua.

$$x^{3}+5x^{2}-6x-30x=180$$

Pahekotia te -6x me -30x, ka -36x.

$$x^{3}+5x^{2}-36x=180$$

Tangohia te 180 mai i ngā taha e rua.

$$x^{3}+5x^{2}-36x-180=0$$

Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau -180, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±180,±90,±60,±45,±36,±30,±20,±18,±15,±12,±10,±9,±6,±5,±4,±3,±2,±1$$

Kimihia tētahi pūtake pērā mā te whakamātau i ngā uara tau tōpū katoa, e tīmata ana i te mea iti rawa mā te uara pū. Mēnā kāore he pūtake tau tōpū e kitea, whakamātauria ngā hautanga.

$$x=-5$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}+5x^{2}-36x-180 ki te x+5, kia riro ko x^{2}-36. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$x^{2}-36=0$$

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te 1 mō te a, te 0 mō te b, me te -36 mō te c i te ture pūrua.

$$x=\frac{0±\sqrt{0^{2}-4\times 1\left(-36\right)}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{0±12}{2}$$

Whakaotia te whārite x^{2}-36=0 ina he tōrunga te ±, ina he tōraro te ±.

$$x=-6 x=6$$

Rārangitia ngā otinga katoa i kitea.

$$x=-5 x=-6 x=6$$