Whakaoti i te 26x(2x-6/3=32x+1x^2-6

$$\frac { 26 x ( 2 x - 6 } { 3 } = 32 x + 1 x ^ { 2 } - 6$$

Whakaoti mō x

$$x = \frac{3 \sqrt{34} + 18}{7} \approx 5.070407955$$

$$x=\frac{18-3\sqrt{34}}{7}\approx 0.072449188$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 3.

$$26x\left(2x-6\right)=96x+3x^{2}-18$$

Whakamahia te āhuatanga tohatoha hei whakarea te 26x ki te 2x-6.

$$52x^{2}-156x=96x+3x^{2}-18$$

Tangohia te 96x mai i ngā taha e rua.

$$52x^{2}-156x-96x=3x^{2}-18$$

Pahekotia te -156x me -96x, ka -252x.

$$52x^{2}-252x=3x^{2}-18$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$52x^{2}-252x-3x^{2}=-18$$

Pahekotia te 52x^{2} me -3x^{2}, ka 49x^{2}.

$$49x^{2}-252x=-18$$

Me tāpiri te 18 ki ngā taha e rua.

$$49x^{2}-252x+18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 49 mō a, -252 mō b, me 18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-252\right)±\sqrt{\left(-252\right)^{2}-4\times 49\times 18}}{2\times 49}$$

Pūrua -252.

$$x=\frac{-\left(-252\right)±\sqrt{63504-4\times 49\times 18}}{2\times 49}$$

Whakareatia -4 ki te 49.

$$x=\frac{-\left(-252\right)±\sqrt{63504-196\times 18}}{2\times 49}$$

Whakareatia -196 ki te 18.

$$x=\frac{-\left(-252\right)±\sqrt{63504-3528}}{2\times 49}$$

Tāpiri 63504 ki te -3528.

$$x=\frac{-\left(-252\right)±\sqrt{59976}}{2\times 49}$$

Tuhia te pūtakerua o te 59976.

$$x=\frac{-\left(-252\right)±42\sqrt{34}}{2\times 49}$$

Ko te tauaro o -252 ko 252.

$$x=\frac{252±42\sqrt{34}}{2\times 49}$$

Whakareatia 2 ki te 49.

$$x=\frac{252±42\sqrt{34}}{98}$$

Nā, me whakaoti te whārite x=\frac{252±42\sqrt{34}}{98} ina he tāpiri te ±. Tāpiri 252 ki te 42\sqrt{34}.

$$x=\frac{42\sqrt{34}+252}{98}$$

Whakawehe 252+42\sqrt{34} ki te 98.

$$x=\frac{3\sqrt{34}+18}{7}$$

Nā, me whakaoti te whārite x=\frac{252±42\sqrt{34}}{98} ina he tango te ±. Tango 42\sqrt{34} mai i 252.

$$x=\frac{252-42\sqrt{34}}{98}$$

Whakawehe 252-42\sqrt{34} ki te 98.

$$x=\frac{18-3\sqrt{34}}{7}$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{34}+18}{7} x=\frac{18-3\sqrt{34}}{7}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 3.

$$26x\left(2x-6\right)=96x+3x^{2}-18$$

Whakamahia te āhuatanga tohatoha hei whakarea te 26x ki te 2x-6.

$$52x^{2}-156x=96x+3x^{2}-18$$

Tangohia te 96x mai i ngā taha e rua.

$$52x^{2}-156x-96x=3x^{2}-18$$

Pahekotia te -156x me -96x, ka -252x.

$$52x^{2}-252x=3x^{2}-18$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$52x^{2}-252x-3x^{2}=-18$$

Pahekotia te 52x^{2} me -3x^{2}, ka 49x^{2}.

$$49x^{2}-252x=-18$$

Whakawehea ngā taha e rua ki te 49.

$$\frac{49x^{2}-252x}{49}=-\frac{18}{49}$$

Mā te whakawehe ki te 49 ka wetekia te whakareanga ki te 49.

$$x^{2}+\left(-\frac{252}{49}\right)x=-\frac{18}{49}$$

Whakahekea te hautanga \frac{-252}{49} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$x^{2}-\frac{36}{7}x=-\frac{18}{49}$$

Whakawehea te -\frac{36}{7}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{18}{7}. Nā, tāpiria te pūrua o te -\frac{18}{7} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{36}{7}x+\left(-\frac{18}{7}\right)^{2}=-\frac{18}{49}+\left(-\frac{18}{7}\right)^{2}$$

Pūruatia -\frac{18}{7} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{36}{7}x+\frac{324}{49}=\frac{-18+324}{49}$$

Tāpiri -\frac{18}{49} ki te \frac{324}{49} 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.

$$x^{2}-\frac{36}{7}x+\frac{324}{49}=\frac{306}{49}$$

Tauwehea x^{2}-\frac{36}{7}x+\frac{324}{49}. 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}.

$$\left(x-\frac{18}{7}\right)^{2}=\frac{306}{49}$$

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

$$\sqrt{\left(x-\frac{18}{7}\right)^{2}}=\sqrt{\frac{306}{49}}$$

Whakarūnātia.

$$x-\frac{18}{7}=\frac{3\sqrt{34}}{7} x-\frac{18}{7}=-\frac{3\sqrt{34}}{7}$$

Me tāpiri \frac{18}{7} ki ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{34}+18}{7} x=\frac{18-3\sqrt{34}}{7}$$