Whakaoti i te 2/3x^2+35=87

$$\frac { 2 } { 3 } x ^ { 2 } + 35 = 87$$

Whakaoti mō x

$$x=\sqrt{78}\approx 8.831760866$$

$$x=-\sqrt{78}\approx -8.831760866$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 35 mai i ngā taha e rua.

$$\frac{2}{3}x^{2}=87-35$$

Tangohia te 35 i te 87, ka 52.

$$\frac{2}{3}x^{2}=52$$

Me whakarea ngā taha e rua ki te \frac{3}{2}, te tau utu o \frac{2}{3}.

$$x^{2}=52\times \frac{3}{2}$$

Whakareatia te 52 ki te \frac{3}{2}, ka 78.

$$x^{2}=78$$

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

$$x=\sqrt{78} x=-\sqrt{78}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 87 mai i ngā taha e rua.

$$\frac{2}{3}x^{2}+35-87=0$$

Tangohia te 87 i te 35, ka -52.

$$\frac{2}{3}x^{2}-52=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{2}{3} mō a, 0 mō b, me -52 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{2}{3}\left(-52\right)}}{2\times \frac{2}{3}}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times \frac{2}{3}\left(-52\right)}}{2\times \frac{2}{3}}$$

Whakareatia -4 ki te \frac{2}{3}.

$$x=\frac{0±\sqrt{-\frac{8}{3}\left(-52\right)}}{2\times \frac{2}{3}}$$

Whakareatia -\frac{8}{3} ki te -52.

$$x=\frac{0±\sqrt{\frac{416}{3}}}{2\times \frac{2}{3}}$$

Tuhia te pūtakerua o te \frac{416}{3}.

$$x=\frac{0±\frac{4\sqrt{78}}{3}}{2\times \frac{2}{3}}$$

Whakareatia 2 ki te \frac{2}{3}.

$$x=\frac{0±\frac{4\sqrt{78}}{3}}{\frac{4}{3}}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{4\sqrt{78}}{3}}{\frac{4}{3}} ina he tāpiri te ±.

$$x=\sqrt{78}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{4\sqrt{78}}{3}}{\frac{4}{3}} ina he tango te ±.

$$x=-\sqrt{78}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{78} x=-\sqrt{78}$$