Whakaoti i te 3x(x-9)-1=2x-6

$$3 x ( x - 9 ) - 1 = 2 x - 6$$

Whakaoti mō x

$$x = \frac{\sqrt{781} + 29}{6} \approx 9.491062871$$

$$x=\frac{29-\sqrt{781}}{6}\approx 0.175603796$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-9.

$$3x^{2}-27x-1=2x-6$$

Tangohia te 2x mai i ngā taha e rua.

$$3x^{2}-27x-1-2x=-6$$

Pahekotia te -27x me -2x, ka -29x.

$$3x^{2}-29x-1=-6$$

Me tāpiri te 6 ki ngā taha e rua.

$$3x^{2}-29x-1+6=0$$

Tāpirihia te -1 ki te 6, ka 5.

$$3x^{2}-29x+5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -29 mō b, me 5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-29\right)±\sqrt{\left(-29\right)^{2}-4\times 3\times 5}}{2\times 3}$$

Pūrua -29.

$$x=\frac{-\left(-29\right)±\sqrt{841-4\times 3\times 5}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-29\right)±\sqrt{841-12\times 5}}{2\times 3}$$

Whakareatia -12 ki te 5.

$$x=\frac{-\left(-29\right)±\sqrt{841-60}}{2\times 3}$$

Tāpiri 841 ki te -60.

$$x=\frac{-\left(-29\right)±\sqrt{781}}{2\times 3}$$

Ko te tauaro o -29 ko 29.

$$x=\frac{29±\sqrt{781}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{29±\sqrt{781}}{6}$$

Nā, me whakaoti te whārite x=\frac{29±\sqrt{781}}{6} ina he tāpiri te ±. Tāpiri 29 ki te \sqrt{781}.

$$x=\frac{\sqrt{781}+29}{6}$$

Nā, me whakaoti te whārite x=\frac{29±\sqrt{781}}{6} ina he tango te ±. Tango \sqrt{781} mai i 29.

$$x=\frac{29-\sqrt{781}}{6}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{781}+29}{6} x=\frac{29-\sqrt{781}}{6}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-9.

$$3x^{2}-27x-1=2x-6$$

Tangohia te 2x mai i ngā taha e rua.

$$3x^{2}-27x-1-2x=-6$$

Pahekotia te -27x me -2x, ka -29x.

$$3x^{2}-29x-1=-6$$

Me tāpiri te 1 ki ngā taha e rua.

$$3x^{2}-29x=-6+1$$

Tāpirihia te -6 ki te 1, ka -5.

$$3x^{2}-29x=-5$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}-29x}{3}=-\frac{5}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$x^{2}-\frac{29}{3}x=-\frac{5}{3}$$

Whakawehea te -\frac{29}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{29}{6}. Nā, tāpiria te pūrua o te -\frac{29}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{29}{3}x+\left(-\frac{29}{6}\right)^{2}=-\frac{5}{3}+\left(-\frac{29}{6}\right)^{2}$$

Pūruatia -\frac{29}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{29}{3}x+\frac{841}{36}=-\frac{5}{3}+\frac{841}{36}$$

Tāpiri -\frac{5}{3} ki te \frac{841}{36} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{29}{3}x+\frac{841}{36}=\frac{781}{36}$$

Tauwehea x^{2}-\frac{29}{3}x+\frac{841}{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}.

$$\left(x-\frac{29}{6}\right)^{2}=\frac{781}{36}$$

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

$$\sqrt{\left(x-\frac{29}{6}\right)^{2}}=\sqrt{\frac{781}{36}}$$

Whakarūnātia.

$$x-\frac{29}{6}=\frac{\sqrt{781}}{6} x-\frac{29}{6}=-\frac{\sqrt{781}}{6}$$

Me tāpiri \frac{29}{6} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{781}+29}{6} x=\frac{29-\sqrt{781}}{6}$$