Whakaoti i te 1064=4+6(x-1)/2*x

$$1064 = \frac { 4 + 6 ( x - 1 ) } { 2 } \cdot x$$

Whakaoti mō x

$$x = -\frac{56}{3} = -18\frac{2}{3} \approx -18.666666667$$

$$x=19$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2128=\left(4+6\left(x-1\right)\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te x-1.

$$2128=\left(4+6x-6\right)x$$

Tangohia te 6 i te 4, ka -2.

$$2128=\left(-2+6x\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2+6x ki te x.

$$2128=-2x+6x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-2x+6x^{2}=2128$$

Tangohia te 2128 mai i ngā taha e rua.

$$-2x+6x^{2}-2128=0$$

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.

$$6x^{2}-2x-2128=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, -2 mō b, me -2128 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 6\left(-2128\right)}}{2\times 6}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times 6\left(-2128\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-\left(-2\right)±\sqrt{4-24\left(-2128\right)}}{2\times 6}$$

Whakareatia -24 ki te -2128.

$$x=\frac{-\left(-2\right)±\sqrt{4+51072}}{2\times 6}$$

Tāpiri 4 ki te 51072.

$$x=\frac{-\left(-2\right)±\sqrt{51076}}{2\times 6}$$

Tuhia te pūtakerua o te 51076.

$$x=\frac{-\left(-2\right)±226}{2\times 6}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±226}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{2±226}{12}$$

Nā, me whakaoti te whārite x=\frac{2±226}{12} ina he tāpiri te ±. Tāpiri 2 ki te 226.

$$x=\frac{228}{12}$$

Whakawehe 228 ki te 12.

$$x=19$$

Nā, me whakaoti te whārite x=\frac{2±226}{12} ina he tango te ±. Tango 226 mai i 2.

$$x=-\frac{224}{12}$$

Whakahekea te hautanga \frac{-224}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=-\frac{56}{3}$$

Kua oti te whārite te whakatau.

$$x=19 x=-\frac{56}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$2128=\left(4+6\left(x-1\right)\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te x-1.

$$2128=\left(4+6x-6\right)x$$

Tangohia te 6 i te 4, ka -2.

$$2128=\left(-2+6x\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2+6x ki te x.

$$2128=-2x+6x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-2x+6x^{2}=2128$$

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.

$$6x^{2}-2x=2128$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}-2x}{6}=\frac{2128}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}+\left(-\frac{2}{6}\right)x=\frac{2128}{6}$$

Whakahekea te hautanga \frac{-2}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{1}{3}x=\frac{2128}{6}$$

Whakahekea te hautanga \frac{2128}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{1}{3}x=\frac{1064}{3}$$

Whakawehea te -\frac{1}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{6}. Nā, tāpiria te pūrua o te -\frac{1}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{3}x+\left(-\frac{1}{6}\right)^{2}=\frac{1064}{3}+\left(-\frac{1}{6}\right)^{2}$$

Pūruatia -\frac{1}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{1064}{3}+\frac{1}{36}$$

Tāpiri \frac{1064}{3} ki te \frac{1}{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.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{12769}{36}$$

Tauwehea x^{2}-\frac{1}{3}x+\frac{1}{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}.

$$\left(x-\frac{1}{6}\right)^{2}=\frac{12769}{36}$$

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

$$\sqrt{\left(x-\frac{1}{6}\right)^{2}}=\sqrt{\frac{12769}{36}}$$

Whakarūnātia.

$$x-\frac{1}{6}=\frac{113}{6} x-\frac{1}{6}=-\frac{113}{6}$$

Me tāpiri \frac{1}{6} ki ngā taha e rua o te whārite.

$$x=19 x=-\frac{56}{3}$$