Whakaoti i te 5x^2-20x+12=x^2+1x-6

$$5 x ^ { 2 } - 20 x + 12 = x ^ { 2 } + 1 x - 6$$

Whakaoti mō x

$$x = \frac{3 \sqrt{17} + 21}{8} \approx 4.17116461$$

$$x = \frac{21 - 3 \sqrt{17}}{8} \approx 1.07883539$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$5x^{2}-20x+12-x^{2}=1x-6$$

Pahekotia te 5x^{2} me -x^{2}, ka 4x^{2}.

$$4x^{2}-20x+12=1x-6$$

Tangohia te 1x mai i ngā taha e rua.

$$4x^{2}-20x+12-x=-6$$

Pahekotia te -20x me -x, ka -21x.

$$4x^{2}-21x+12=-6$$

Me tāpiri te 6 ki ngā taha e rua.

$$4x^{2}-21x+12+6=0$$

Tāpirihia te 12 ki te 6, ka 18.

$$4x^{2}-21x+18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, -21 mō b, me 18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4\times 4\times 18}}{2\times 4}$$

Pūrua -21.

$$x=\frac{-\left(-21\right)±\sqrt{441-4\times 4\times 18}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-\left(-21\right)±\sqrt{441-16\times 18}}{2\times 4}$$

Whakareatia -16 ki te 18.

$$x=\frac{-\left(-21\right)±\sqrt{441-288}}{2\times 4}$$

Tāpiri 441 ki te -288.

$$x=\frac{-\left(-21\right)±\sqrt{153}}{2\times 4}$$

Tuhia te pūtakerua o te 153.

$$x=\frac{-\left(-21\right)±3\sqrt{17}}{2\times 4}$$

Ko te tauaro o -21 ko 21.

$$x=\frac{21±3\sqrt{17}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{21±3\sqrt{17}}{8}$$

Nā, me whakaoti te whārite x=\frac{21±3\sqrt{17}}{8} ina he tāpiri te ±. Tāpiri 21 ki te 3\sqrt{17}.

$$x=\frac{3\sqrt{17}+21}{8}$$

Nā, me whakaoti te whārite x=\frac{21±3\sqrt{17}}{8} ina he tango te ±. Tango 3\sqrt{17} mai i 21.

$$x=\frac{21-3\sqrt{17}}{8}$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{17}+21}{8} x=\frac{21-3\sqrt{17}}{8}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$5x^{2}-20x+12-x^{2}=1x-6$$

Pahekotia te 5x^{2} me -x^{2}, ka 4x^{2}.

$$4x^{2}-20x+12=1x-6$$

Tangohia te 1x mai i ngā taha e rua.

$$4x^{2}-20x+12-x=-6$$

Pahekotia te -20x me -x, ka -21x.

$$4x^{2}-21x+12=-6$$

Tangohia te 12 mai i ngā taha e rua.

$$4x^{2}-21x=-6-12$$

Tangohia te 12 i te -6, ka -18.

$$4x^{2}-21x=-18$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}-21x}{4}=-\frac{18}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$x^{2}-\frac{21}{4}x=-\frac{18}{4}$$

Whakahekea te hautanga \frac{-18}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{21}{4}x=-\frac{9}{2}$$

Whakawehea te -\frac{21}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{21}{8}. Nā, tāpiria te pūrua o te -\frac{21}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{21}{4}x+\left(-\frac{21}{8}\right)^{2}=-\frac{9}{2}+\left(-\frac{21}{8}\right)^{2}$$

Pūruatia -\frac{21}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{21}{4}x+\frac{441}{64}=-\frac{9}{2}+\frac{441}{64}$$

Tāpiri -\frac{9}{2} ki te \frac{441}{64} 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.

$$x^{2}-\frac{21}{4}x+\frac{441}{64}=\frac{153}{64}$$

Tauwehea x^{2}-\frac{21}{4}x+\frac{441}{64}. 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}.

$$\left(x-\frac{21}{8}\right)^{2}=\frac{153}{64}$$

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

$$\sqrt{\left(x-\frac{21}{8}\right)^{2}}=\sqrt{\frac{153}{64}}$$

Whakarūnātia.

$$x-\frac{21}{8}=\frac{3\sqrt{17}}{8} x-\frac{21}{8}=-\frac{3\sqrt{17}}{8}$$

Me tāpiri \frac{21}{8} ki ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{17}+21}{8} x=\frac{21-3\sqrt{17}}{8}$$