Whakaoti i te x^2-9=160

$${ x }^{ 2 } -9=160$$

Whakaoti mō x

$$x=13$$

$$x=-13$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tangohia te 160 mai i ngā taha e rua.

$$x^{2}-9-160=0$$

Tangohia te 160 i te -9, ka -169.

$$x^{2}-169=0$$

Whakaarohia te x^{2}-169. Tuhia anō te x^{2}-169 hei x^{2}-13^{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).

$$\left(x-13\right)\left(x+13\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-13=0 me te x+13=0.

$$x=13 x=-13$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 9 ki ngā taha e rua.

$$x^{2}=160+9$$

Tāpirihia te 160 ki te 9, ka 169.

$$x^{2}=169$$

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

$$x=13 x=-13$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 160 mai i ngā taha e rua.

$$x^{2}-9-160=0$$

Tangohia te 160 i te -9, ka -169.

$$x^{2}-169=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -169 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-169\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-169\right)}}{2}$$

Whakareatia -4 ki te -169.

$$x=\frac{0±\sqrt{676}}{2}$$

Tuhia te pūtakerua o te 676.

$$x=\frac{0±26}{2}$$

Nā, me whakaoti te whārite x=\frac{0±26}{2} ina he tāpiri te ±. Whakawehe 26 ki te 2.

$$x=13$$

Nā, me whakaoti te whārite x=\frac{0±26}{2} ina he tango te ±. Whakawehe -26 ki te 2.

$$x=-13$$

Kua oti te whārite te whakatau.

$$x=13 x=-13$$