Whakaoti i te (6x-11)^2=12x

$$( 6 x - 11 ) ^ { 2 } = 12 x$$

Whakaoti mō x

$$x=\frac{\sqrt{23}}{6}+2\approx 2.799305254$$

$$x=-\frac{\sqrt{23}}{6}+2\approx 1.200694746$$

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(6x-11\right)^{2}.

$$36x^{2}-132x+121=12x$$

Tangohia te 12x mai i ngā taha e rua.

$$36x^{2}-132x+121-12x=0$$

Pahekotia te -132x me -12x, ka -144x.

$$36x^{2}-144x+121=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 36 mō a, -144 mō b, me 121 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-144\right)±\sqrt{\left(-144\right)^{2}-4\times 36\times 121}}{2\times 36}$$

Pūrua -144.

$$x=\frac{-\left(-144\right)±\sqrt{20736-4\times 36\times 121}}{2\times 36}$$

Whakareatia -4 ki te 36.

$$x=\frac{-\left(-144\right)±\sqrt{20736-144\times 121}}{2\times 36}$$

Whakareatia -144 ki te 121.

$$x=\frac{-\left(-144\right)±\sqrt{20736-17424}}{2\times 36}$$

Tāpiri 20736 ki te -17424.

$$x=\frac{-\left(-144\right)±\sqrt{3312}}{2\times 36}$$

Tuhia te pūtakerua o te 3312.

$$x=\frac{-\left(-144\right)±12\sqrt{23}}{2\times 36}$$

Ko te tauaro o -144 ko 144.

$$x=\frac{144±12\sqrt{23}}{2\times 36}$$

Whakareatia 2 ki te 36.

$$x=\frac{144±12\sqrt{23}}{72}$$

Nā, me whakaoti te whārite x=\frac{144±12\sqrt{23}}{72} ina he tāpiri te ±. Tāpiri 144 ki te 12\sqrt{23}.

$$x=\frac{12\sqrt{23}+144}{72}$$

Whakawehe 144+12\sqrt{23} ki te 72.

$$x=\frac{\sqrt{23}}{6}+2$$

Nā, me whakaoti te whārite x=\frac{144±12\sqrt{23}}{72} ina he tango te ±. Tango 12\sqrt{23} mai i 144.

$$x=\frac{144-12\sqrt{23}}{72}$$

Whakawehe 144-12\sqrt{23} ki te 72.

$$x=-\frac{\sqrt{23}}{6}+2$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{23}}{6}+2 x=-\frac{\sqrt{23}}{6}+2$$

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(6x-11\right)^{2}.

$$36x^{2}-132x+121=12x$$

Tangohia te 12x mai i ngā taha e rua.

$$36x^{2}-132x+121-12x=0$$

Pahekotia te -132x me -12x, ka -144x.

$$36x^{2}-144x+121=0$$

Tangohia te 121 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$36x^{2}-144x=-121$$

Whakawehea ngā taha e rua ki te 36.

$$\frac{36x^{2}-144x}{36}=-\frac{121}{36}$$

Mā te whakawehe ki te 36 ka wetekia te whakareanga ki te 36.

$$x^{2}+\left(-\frac{144}{36}\right)x=-\frac{121}{36}$$

Whakawehe -144 ki te 36.

$$x^{2}-4x=-\frac{121}{36}$$

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

$$x^{2}-4x+\left(-2\right)^{2}=-\frac{121}{36}+\left(-2\right)^{2}$$

Pūrua -2.

$$x^{2}-4x+4=-\frac{121}{36}+4$$

Tāpiri -\frac{121}{36} ki te 4.

$$x^{2}-4x+4=\frac{23}{36}$$

Tauwehea x^{2}-4x+4. 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}.

$$\left(x-2\right)^{2}=\frac{23}{36}$$

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

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{\frac{23}{36}}$$

Whakarūnātia.

$$x-2=\frac{\sqrt{23}}{6} x-2=-\frac{\sqrt{23}}{6}$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{23}}{6}+2 x=-\frac{\sqrt{23}}{6}+2$$