Whakaoti i te 10x^2-56=88-6x^2

$$10 x ^ { 2 } - 56 = 88 - 6 x ^ { 2 }$$

Whakaoti mō x

$$x=3$$

$$x=-3$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tangohia te 88 mai i ngā taha e rua.

$$10x^{2}-56-88=-6x^{2}$$

Tangohia te 88 i te -56, ka -144.

$$10x^{2}-144=-6x^{2}$$

Me tāpiri te 6x^{2} ki ngā taha e rua.

$$10x^{2}-144+6x^{2}=0$$

Pahekotia te 10x^{2} me 6x^{2}, ka 16x^{2}.

$$16x^{2}-144=0$$

Whakawehea ngā taha e rua ki te 16.

$$x^{2}-9=0$$

Whakaarohia te x^{2}-9. Tuhia anō te x^{2}-9 hei x^{2}-3^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-3\right)\left(x+3\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-3=0 me te x+3=0.

$$x=3 x=-3$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 6x^{2} ki ngā taha e rua.

$$10x^{2}-56+6x^{2}=88$$

Pahekotia te 10x^{2} me 6x^{2}, ka 16x^{2}.

$$16x^{2}-56=88$$

Me tāpiri te 56 ki ngā taha e rua.

$$16x^{2}=88+56$$

Tāpirihia te 88 ki te 56, ka 144.

$$16x^{2}=144$$

Whakawehea ngā taha e rua ki te 16.

$$x^{2}=\frac{144}{16}$$

Whakawehea te 144 ki te 16, kia riro ko 9.

$$x^{2}=9$$

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

$$x=3 x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 88 mai i ngā taha e rua.

$$10x^{2}-56-88=-6x^{2}$$

Tangohia te 88 i te -56, ka -144.

$$10x^{2}-144=-6x^{2}$$

Me tāpiri te 6x^{2} ki ngā taha e rua.

$$10x^{2}-144+6x^{2}=0$$

Pahekotia te 10x^{2} me 6x^{2}, ka 16x^{2}.

$$16x^{2}-144=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 16 mō a, 0 mō b, me -144 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-144\right)}}{2\times 16}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-144\right)}}{2\times 16}$$

Whakareatia -4 ki te 16.

$$x=\frac{0±\sqrt{-64\left(-144\right)}}{2\times 16}$$

Whakareatia -64 ki te -144.

$$x=\frac{0±\sqrt{9216}}{2\times 16}$$

Tuhia te pūtakerua o te 9216.

$$x=\frac{0±96}{2\times 16}$$

Whakareatia 2 ki te 16.

$$x=\frac{0±96}{32}$$

Nā, me whakaoti te whārite x=\frac{0±96}{32} ina he tāpiri te ±. Whakawehe 96 ki te 32.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{0±96}{32} ina he tango te ±. Whakawehe -96 ki te 32.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=3 x=-3$$