Whakaoti i te 5=1/2250x^2+1/250left(x+02right)^2

$$5 = \frac{ 1 }{ 2 } 250 { x }^{ 2 } + \frac{ 1 }{ 2 } 50 { \left(x+02 \right) }^{ 2 }$$

Whakaoti mō x

$$x=\frac{\sqrt{30}}{30}\approx 0.182574186$$

$$x=-\frac{\sqrt{30}}{30}\approx -0.182574186$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia te \frac{1}{2} ki te 250, ka 125.

$$5=125x^{2}+\frac{1}{2}\times 50\left(x+0\times 2\right)^{2}$$

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

$$5=125x^{2}+25\left(x+0\times 2\right)^{2}$$

Whakareatia te 0 ki te 2, ka 0.

$$5=125x^{2}+25\left(x+0\right)^{2}$$

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

$$5=125x^{2}+25x^{2}$$

Pahekotia te 125x^{2} me 25x^{2}, ka 150x^{2}.

$$5=150x^{2}$$

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

$$150x^{2}=5$$

Whakawehea ngā taha e rua ki te 150.

$$x^{2}=\frac{5}{150}$$

Whakahekea te hautanga \frac{5}{150} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$x^{2}=\frac{1}{30}$$

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

$$x=\frac{\sqrt{30}}{30} x=-\frac{\sqrt{30}}{30}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te \frac{1}{2} ki te 250, ka 125.

$$5=125x^{2}+\frac{1}{2}\times 50\left(x+0\times 2\right)^{2}$$

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

$$5=125x^{2}+25\left(x+0\times 2\right)^{2}$$

Whakareatia te 0 ki te 2, ka 0.

$$5=125x^{2}+25\left(x+0\right)^{2}$$

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

$$5=125x^{2}+25x^{2}$$

Pahekotia te 125x^{2} me 25x^{2}, ka 150x^{2}.

$$5=150x^{2}$$

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

$$150x^{2}=5$$

Tangohia te 5 mai i ngā taha e rua.

$$150x^{2}-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 150 mō a, 0 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 150\left(-5\right)}}{2\times 150}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 150\left(-5\right)}}{2\times 150}$$

Whakareatia -4 ki te 150.

$$x=\frac{0±\sqrt{-600\left(-5\right)}}{2\times 150}$$

Whakareatia -600 ki te -5.

$$x=\frac{0±\sqrt{3000}}{2\times 150}$$

Tuhia te pūtakerua o te 3000.

$$x=\frac{0±10\sqrt{30}}{2\times 150}$$

Whakareatia 2 ki te 150.

$$x=\frac{0±10\sqrt{30}}{300}$$

Nā, me whakaoti te whārite x=\frac{0±10\sqrt{30}}{300} ina he tāpiri te ±.

$$x=\frac{\sqrt{30}}{30}$$

Nā, me whakaoti te whārite x=\frac{0±10\sqrt{30}}{300} ina he tango te ±.

$$x=-\frac{\sqrt{30}}{30}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{30}}{30} x=-\frac{\sqrt{30}}{30}$$