Whakaoti i te 21left(x-2right)^2-(x-2)=2

$$21 { \left(x-2 \right) }^{ 2 } -(x-2)=2$$

Whakaoti mō x

$$x = \frac{12}{7} = 1\frac{5}{7} \approx 1.714285714$$

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-2\right)^{2}.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 21 ki te x^{2}-4x+4.

$$21x^{2}-84x+84-\left(x-2\right)=2$$

Hei kimi i te tauaro o x-2, kimihia te tauaro o ia taurangi.

$$21x^{2}-84x+84-x+2=2$$

Pahekotia te -84x me -x, ka -85x.

$$21x^{2}-85x+84+2=2$$

Tāpirihia te 84 ki te 2, ka 86.

$$21x^{2}-85x+86=2$$

Tangohia te 2 mai i ngā taha e rua.

$$21x^{2}-85x+86-2=0$$

Tangohia te 2 i te 86, ka 84.

$$21x^{2}-85x+84=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 21 mō a, -85 mō b, me 84 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-85\right)±\sqrt{\left(-85\right)^{2}-4\times 21\times 84}}{2\times 21}$$

Pūrua -85.

$$x=\frac{-\left(-85\right)±\sqrt{7225-4\times 21\times 84}}{2\times 21}$$

Whakareatia -4 ki te 21.

$$x=\frac{-\left(-85\right)±\sqrt{7225-84\times 84}}{2\times 21}$$

Whakareatia -84 ki te 84.

$$x=\frac{-\left(-85\right)±\sqrt{7225-7056}}{2\times 21}$$

Tāpiri 7225 ki te -7056.

$$x=\frac{-\left(-85\right)±\sqrt{169}}{2\times 21}$$

Tuhia te pūtakerua o te 169.

$$x=\frac{-\left(-85\right)±13}{2\times 21}$$

Ko te tauaro o -85 ko 85.

$$x=\frac{85±13}{2\times 21}$$

Whakareatia 2 ki te 21.

$$x=\frac{85±13}{42}$$

Nā, me whakaoti te whārite x=\frac{85±13}{42} ina he tāpiri te ±. Tāpiri 85 ki te 13.

$$x=\frac{98}{42}$$

Whakahekea te hautanga \frac{98}{42} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$x=\frac{7}{3}$$

Nā, me whakaoti te whārite x=\frac{85±13}{42} ina he tango te ±. Tango 13 mai i 85.

$$x=\frac{72}{42}$$

Whakahekea te hautanga \frac{72}{42} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x=\frac{12}{7}$$

Kua oti te whārite te whakatau.

$$x=\frac{7}{3} x=\frac{12}{7}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-2\right)^{2}.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 21 ki te x^{2}-4x+4.

$$21x^{2}-84x+84-\left(x-2\right)=2$$

Hei kimi i te tauaro o x-2, kimihia te tauaro o ia taurangi.

$$21x^{2}-84x+84-x+2=2$$

Pahekotia te -84x me -x, ka -85x.

$$21x^{2}-85x+84+2=2$$

Tāpirihia te 84 ki te 2, ka 86.

$$21x^{2}-85x+86=2$$

Tangohia te 86 mai i ngā taha e rua.

$$21x^{2}-85x=2-86$$

Tangohia te 86 i te 2, ka -84.

$$21x^{2}-85x=-84$$

Whakawehea ngā taha e rua ki te 21.

$$\frac{21x^{2}-85x}{21}=-\frac{84}{21}$$

Mā te whakawehe ki te 21 ka wetekia te whakareanga ki te 21.

$$x^{2}-\frac{85}{21}x=-\frac{84}{21}$$

Whakawehe -84 ki te 21.

$$x^{2}-\frac{85}{21}x=-4$$

Whakawehea te -\frac{85}{21}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{85}{42}. Nā, tāpiria te pūrua o te -\frac{85}{42} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{85}{21}x+\left(-\frac{85}{42}\right)^{2}=-4+\left(-\frac{85}{42}\right)^{2}$$

Pūruatia -\frac{85}{42} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{85}{21}x+\frac{7225}{1764}=-4+\frac{7225}{1764}$$

Tāpiri -4 ki te \frac{7225}{1764}.

$$x^{2}-\frac{85}{21}x+\frac{7225}{1764}=\frac{169}{1764}$$

Tauwehea x^{2}-\frac{85}{21}x+\frac{7225}{1764}. 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}.

$$\left(x-\frac{85}{42}\right)^{2}=\frac{169}{1764}$$

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

$$\sqrt{\left(x-\frac{85}{42}\right)^{2}}=\sqrt{\frac{169}{1764}}$$

Whakarūnātia.

$$x-\frac{85}{42}=\frac{13}{42} x-\frac{85}{42}=-\frac{13}{42}$$

Me tāpiri \frac{85}{42} ki ngā taha e rua o te whārite.

$$x=\frac{7}{3} x=\frac{12}{7}$$