Whakaoti i te left(1.18-xright)^2=0.8x

$${ \left(1.18-x \right) }^{ 2 } =0.8x$$

Whakaoti mō x

$$x=\frac{\sqrt{690}}{25}+1.58\approx 2.630714043$$

$$x=-\frac{\sqrt{690}}{25}+1.58\approx 0.529285957$$

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(1.18-x\right)^{2}.

$$1.3924-2.36x+x^{2}=0.8x$$

Tangohia te 0.8x mai i ngā taha e rua.

$$1.3924-2.36x+x^{2}-0.8x=0$$

Pahekotia te -2.36x me -0.8x, ka -3.16x.

$$1.3924-3.16x+x^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x^{2}-3.16x+1.3924=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -3.16 mō b, me 1.3924 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3.16\right)±\sqrt{\left(-3.16\right)^{2}-4\times 1.3924}}{2}$$

Pūruatia -3.16 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-3.16\right)±\sqrt{9.9856-4\times 1.3924}}{2}$$

Whakareatia -4 ki te 1.3924.

$$x=\frac{-\left(-3.16\right)±\sqrt{\frac{6241-3481}{625}}}{2}$$

Tāpiri 9.9856 ki te -5.5696 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.

$$x=\frac{-\left(-3.16\right)±\sqrt{4.416}}{2}$$

Tuhia te pūtakerua o te 4.416.

$$x=\frac{-\left(-3.16\right)±\frac{2\sqrt{690}}{25}}{2}$$

Ko te tauaro o -3.16 ko 3.16.

$$x=\frac{3.16±\frac{2\sqrt{690}}{25}}{2}$$

Nā, me whakaoti te whārite x=\frac{3.16±\frac{2\sqrt{690}}{25}}{2} ina he tāpiri te ±. Tāpiri 3.16 ki te \frac{2\sqrt{690}}{25}.

$$x=\frac{2\sqrt{690}+79}{2\times 25}$$

Whakawehe \frac{79+2\sqrt{690}}{25} ki te 2.

$$x=\frac{\sqrt{690}}{25}+\frac{79}{50}$$

Nā, me whakaoti te whārite x=\frac{3.16±\frac{2\sqrt{690}}{25}}{2} ina he tango te ±. Tango \frac{2\sqrt{690}}{25} mai i 3.16.

$$x=\frac{79-2\sqrt{690}}{2\times 25}$$

Whakawehe \frac{79-2\sqrt{690}}{25} ki te 2.

$$x=-\frac{\sqrt{690}}{25}+\frac{79}{50}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{690}}{25}+\frac{79}{50} x=-\frac{\sqrt{690}}{25}+\frac{79}{50}$$

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(1.18-x\right)^{2}.

$$1.3924-2.36x+x^{2}=0.8x$$

Tangohia te 0.8x mai i ngā taha e rua.

$$1.3924-2.36x+x^{2}-0.8x=0$$

Pahekotia te -2.36x me -0.8x, ka -3.16x.

$$1.3924-3.16x+x^{2}=0$$

Tangohia te 1.3924 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-3.16x+x^{2}=-1.3924$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$x^{2}-3.16x=-1.3924$$

Whakawehea te -3.16, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1.58. Nā, tāpiria te pūrua o te -1.58 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-3.16x+\left(-1.58\right)^{2}=-1.3924+\left(-1.58\right)^{2}$$

Pūruatia -1.58 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3.16x+2.4964=\frac{-3481+6241}{2500}$$

Tāpiri -1.3924 ki te 2.4964 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.

$$x^{2}-3.16x+2.4964=1.104$$

Tauwehea x^{2}-3.16x+2.4964. 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}.

$$\left(x-1.58\right)^{2}=1.104$$

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

$$\sqrt{\left(x-1.58\right)^{2}}=\sqrt{1.104}$$

Whakarūnātia.

$$x-1.58=\frac{\sqrt{690}}{25} x-1.58=-\frac{\sqrt{690}}{25}$$

Me tāpiri 1.58 ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{690}}{25}+\frac{79}{50} x=-\frac{\sqrt{690}}{25}+\frac{79}{50}$$