Whakaoti i te 6w^2-13=15-3w^2

$$6 w ^ { 2 } - 13 = 15 - 3 w ^ { 2 }$$

Whakaoti mō w

$$w = \frac{2 \sqrt{7}}{3} \approx 1.763834207$$

$$w = -\frac{2 \sqrt{7}}{3} \approx -1.763834207$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 3w^{2} ki ngā taha e rua.

$$6w^{2}-13+3w^{2}=15$$

Pahekotia te 6w^{2} me 3w^{2}, ka 9w^{2}.

$$9w^{2}-13=15$$

Me tāpiri te 13 ki ngā taha e rua.

$$9w^{2}=15+13$$

Tāpirihia te 15 ki te 13, ka 28.

$$9w^{2}=28$$

Whakawehea ngā taha e rua ki te 9.

$$w^{2}=\frac{28}{9}$$

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

$$w=\frac{2\sqrt{7}}{3} w=-\frac{2\sqrt{7}}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 15 mai i ngā taha e rua.

$$6w^{2}-13-15=-3w^{2}$$

Tangohia te 15 i te -13, ka -28.

$$6w^{2}-28=-3w^{2}$$

Me tāpiri te 3w^{2} ki ngā taha e rua.

$$6w^{2}-28+3w^{2}=0$$

Pahekotia te 6w^{2} me 3w^{2}, ka 9w^{2}.

$$9w^{2}-28=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, 0 mō b, me -28 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 9\left(-28\right)}}{2\times 9}$$

Pūrua 0.

$$w=\frac{0±\sqrt{-4\times 9\left(-28\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$w=\frac{0±\sqrt{-36\left(-28\right)}}{2\times 9}$$

Whakareatia -36 ki te -28.

$$w=\frac{0±\sqrt{1008}}{2\times 9}$$

Tuhia te pūtakerua o te 1008.

$$w=\frac{0±12\sqrt{7}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$w=\frac{0±12\sqrt{7}}{18}$$

Nā, me whakaoti te whārite w=\frac{0±12\sqrt{7}}{18} ina he tāpiri te ±.

$$w=\frac{2\sqrt{7}}{3}$$

Nā, me whakaoti te whārite w=\frac{0±12\sqrt{7}}{18} ina he tango te ±.

$$w=-\frac{2\sqrt{7}}{3}$$

Kua oti te whārite te whakatau.

$$w=\frac{2\sqrt{7}}{3} w=-\frac{2\sqrt{7}}{3}$$