Whakaoti i te 5=1/2*20*x^2+1/2*50(x+02)^2

$$5 = \frac { 1 } { 2 } \cdot 20 \cdot x ^ { 2 } + \frac { 1 } { 2 } \cdot 50 ( x + 02 ) ^ { 2 }$$

Whakaoti mō x

$$x=\frac{\sqrt{7}}{7}\approx 0.377964473$$

$$x=-\frac{\sqrt{7}}{7}\approx -0.377964473$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te \frac{1}{2} ki te 20, ka 10.

$$5=10x^{2}+\frac{1}{2}\times 50\left(x+0\times 2\right)^{2}$$

Whakareatia te \frac{1}{2} ki te 50, ka 25.

$$5=10x^{2}+25\left(x+0\times 2\right)^{2}$$

Whakareatia te 0 ki te 2, ka 0.

$$5=10x^{2}+25\left(x+0\right)^{2}$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$5=10x^{2}+25x^{2}$$

Pahekotia te 10x^{2} me 25x^{2}, ka 35x^{2}.

$$5=35x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$35x^{2}=5$$

Whakawehea ngā taha e rua ki te 35.

$$x^{2}=\frac{5}{35}$$

Whakahekea te hautanga \frac{5}{35} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$x^{2}=\frac{1}{7}$$

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

$$x=\frac{\sqrt{7}}{7} x=-\frac{\sqrt{7}}{7}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te \frac{1}{2} ki te 20, ka 10.

$$5=10x^{2}+\frac{1}{2}\times 50\left(x+0\times 2\right)^{2}$$

Whakareatia te \frac{1}{2} ki te 50, ka 25.

$$5=10x^{2}+25\left(x+0\times 2\right)^{2}$$

Whakareatia te 0 ki te 2, ka 0.

$$5=10x^{2}+25\left(x+0\right)^{2}$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$5=10x^{2}+25x^{2}$$

Pahekotia te 10x^{2} me 25x^{2}, ka 35x^{2}.

$$5=35x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$35x^{2}=5$$

Tangohia te 5 mai i ngā taha e rua.

$$35x^{2}-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 35 mō a, 0 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 35\left(-5\right)}}{2\times 35}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 35\left(-5\right)}}{2\times 35}$$

Whakareatia -4 ki te 35.

$$x=\frac{0±\sqrt{-140\left(-5\right)}}{2\times 35}$$

Whakareatia -140 ki te -5.

$$x=\frac{0±\sqrt{700}}{2\times 35}$$

Tuhia te pūtakerua o te 700.

$$x=\frac{0±10\sqrt{7}}{2\times 35}$$

Whakareatia 2 ki te 35.

$$x=\frac{0±10\sqrt{7}}{70}$$

Nā, me whakaoti te whārite x=\frac{0±10\sqrt{7}}{70} ina he tāpiri te ±.

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

Nā, me whakaoti te whārite x=\frac{0±10\sqrt{7}}{70} ina he tango te ±.

$$x=-\frac{\sqrt{7}}{7}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{7}}{7} x=-\frac{\sqrt{7}}{7}$$