Whakaoti i te (x-1)^2=16x

$$( x - 1 ) ^ { 2 } = 16 x$$

Whakaoti mō x

$$x=4\sqrt{5}+9\approx 17.94427191$$

$$x=9-4\sqrt{5}\approx 0.05572809$$

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-1\right)^{2}.

$$x^{2}-2x+1=16x$$

Tangohia te 16x mai i ngā taha e rua.

$$x^{2}-2x+1-16x=0$$

Pahekotia te -2x me -16x, ka -18x.

$$x^{2}-18x+1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -18 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua -18.

$$x=\frac{-\left(-18\right)±\sqrt{324-4}}{2}$$

Tāpiri 324 ki te -4.

$$x=\frac{-\left(-18\right)±\sqrt{320}}{2}$$

Tuhia te pūtakerua o te 320.

$$x=\frac{-\left(-18\right)±8\sqrt{5}}{2}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±8\sqrt{5}}{2}$$

Nā, me whakaoti te whārite x=\frac{18±8\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri 18 ki te 8\sqrt{5}.

$$x=\frac{8\sqrt{5}+18}{2}$$

Whakawehe 18+8\sqrt{5} ki te 2.

$$x=4\sqrt{5}+9$$

Nā, me whakaoti te whārite x=\frac{18±8\sqrt{5}}{2} ina he tango te ±. Tango 8\sqrt{5} mai i 18.

$$x=\frac{18-8\sqrt{5}}{2}$$

Whakawehe 18-8\sqrt{5} ki te 2.

$$x=9-4\sqrt{5}$$

Kua oti te whārite te whakatau.

$$x=4\sqrt{5}+9 x=9-4\sqrt{5}$$

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-1\right)^{2}.

$$x^{2}-2x+1=16x$$

Tangohia te 16x mai i ngā taha e rua.

$$x^{2}-2x+1-16x=0$$

Pahekotia te -2x me -16x, ka -18x.

$$x^{2}-18x+1=0$$

Tangohia te 1 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-18x=-1$$

Whakawehea te -18, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -9. Nā, tāpiria te pūrua o te -9 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-18x+\left(-9\right)^{2}=-1+\left(-9\right)^{2}$$

Pūrua -9.

$$x^{2}-18x+81=-1+81$$

Tāpiri -1 ki te 81.

$$x^{2}-18x+81=80$$

Tauwehea te x^{2}-18x+81. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-9\right)^{2}=80$$

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

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{80}$$

Whakarūnātia.

$$x-9=4\sqrt{5} x-9=-4\sqrt{5}$$

Me tāpiri 9 ki ngā taha e rua o te whārite.

$$x=4\sqrt{5}+9 x=9-4\sqrt{5}$$