Whakaoti i te x^2-14=5x+67-5x

$$x ^ { 2 } - 14 = 5 x + 67 - 5 x$$

Whakaoti mō x

$$x=9$$

$$x=-9$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Pahekotia te 5x me -5x, ka 0.

$$x^{2}-14=67$$

Tangohia te 67 mai i ngā taha e rua.

$$x^{2}-14-67=0$$

Tangohia te 67 i te -14, ka -81.

$$x^{2}-81=0$$

Whakaarohia te x^{2}-81. Tuhia anō te x^{2}-81 hei x^{2}-9^{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).

$$\left(x-9\right)\left(x+9\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-9=0 me te x+9=0.

$$x=9 x=-9$$

Ngā Upane mā te Kimi Pūtakerua

Pahekotia te 5x me -5x, ka 0.

$$x^{2}-14=67$$

Me tāpiri te 14 ki ngā taha e rua.

$$x^{2}=67+14$$

Tāpirihia te 67 ki te 14, ka 81.

$$x^{2}=81$$

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

$$x=9 x=-9$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 5x me -5x, ka 0.

$$x^{2}-14=67$$

Tangohia te 67 mai i ngā taha e rua.

$$x^{2}-14-67=0$$

Tangohia te 67 i te -14, ka -81.

$$x^{2}-81=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -81 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

Whakareatia -4 ki te -81.

$$x=\frac{0±\sqrt{324}}{2}$$

Tuhia te pūtakerua o te 324.

$$x=\frac{0±18}{2}$$

Nā, me whakaoti te whārite x=\frac{0±18}{2} ina he tāpiri te ±. Whakawehe 18 ki te 2.

$$x=9$$

Nā, me whakaoti te whārite x=\frac{0±18}{2} ina he tango te ±. Whakawehe -18 ki te 2.

$$x=-9$$

Kua oti te whārite te whakatau.

$$x=9 x=-9$$