Whakaoti i te 3x(x-4)=4x+(x-2)

$$3 x ( x - 4 ) = 4 x + ( x - 2 )$$

Whakaoti mō x

$$x = \frac{\sqrt{265} + 17}{6} \approx 5.546470099$$

$$x=\frac{17-\sqrt{265}}{6}\approx 0.120196567$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-4.

$$3x^{2}-12x=4x+x-2$$

Pahekotia te 4x me x, ka 5x.

$$3x^{2}-12x=5x-2$$

Tangohia te 5x mai i ngā taha e rua.

$$3x^{2}-12x-5x=-2$$

Pahekotia te -12x me -5x, ka -17x.

$$3x^{2}-17x=-2$$

Me tāpiri te 2 ki ngā taha e rua.

$$3x^{2}-17x+2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -17 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 3\times 2}}{2\times 3}$$

Pūrua -17.

$$x=\frac{-\left(-17\right)±\sqrt{289-4\times 3\times 2}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-17\right)±\sqrt{289-12\times 2}}{2\times 3}$$

Whakareatia -12 ki te 2.

$$x=\frac{-\left(-17\right)±\sqrt{289-24}}{2\times 3}$$

Tāpiri 289 ki te -24.

$$x=\frac{-\left(-17\right)±\sqrt{265}}{2\times 3}$$

Ko te tauaro o -17 ko 17.

$$x=\frac{17±\sqrt{265}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{17±\sqrt{265}}{6}$$

Nā, me whakaoti te whārite x=\frac{17±\sqrt{265}}{6} ina he tāpiri te ±. Tāpiri 17 ki te \sqrt{265}.

$$x=\frac{\sqrt{265}+17}{6}$$

Nā, me whakaoti te whārite x=\frac{17±\sqrt{265}}{6} ina he tango te ±. Tango \sqrt{265} mai i 17.

$$x=\frac{17-\sqrt{265}}{6}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{265}+17}{6} x=\frac{17-\sqrt{265}}{6}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-4.

$$3x^{2}-12x=4x+x-2$$

Pahekotia te 4x me x, ka 5x.

$$3x^{2}-12x=5x-2$$

Tangohia te 5x mai i ngā taha e rua.

$$3x^{2}-12x-5x=-2$$

Pahekotia te -12x me -5x, ka -17x.

$$3x^{2}-17x=-2$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}-17x}{3}=-\frac{2}{3}$$

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

$$x^{2}-\frac{17}{3}x=-\frac{2}{3}$$

Whakawehea te -\frac{17}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{17}{6}. Nā, tāpiria te pūrua o te -\frac{17}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{17}{3}x+\left(-\frac{17}{6}\right)^{2}=-\frac{2}{3}+\left(-\frac{17}{6}\right)^{2}$$

Pūruatia -\frac{17}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{17}{3}x+\frac{289}{36}=-\frac{2}{3}+\frac{289}{36}$$

Tāpiri -\frac{2}{3} ki te \frac{289}{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.

$$x^{2}-\frac{17}{3}x+\frac{289}{36}=\frac{265}{36}$$

Tauwehea x^{2}-\frac{17}{3}x+\frac{289}{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}.

$$\left(x-\frac{17}{6}\right)^{2}=\frac{265}{36}$$

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

$$\sqrt{\left(x-\frac{17}{6}\right)^{2}}=\sqrt{\frac{265}{36}}$$

Whakarūnātia.

$$x-\frac{17}{6}=\frac{\sqrt{265}}{6} x-\frac{17}{6}=-\frac{\sqrt{265}}{6}$$

Me tāpiri \frac{17}{6} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{265}+17}{6} x=\frac{17-\sqrt{265}}{6}$$