Whakaoti i te 9x^2+7=8

$$9 x ^ { 2 } + 7 = 8$$

Whakaoti mō x

$$x=\frac{1}{3}\approx 0.333333333$$

$$x=-\frac{1}{3}\approx -0.333333333$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tangohia te 8 mai i ngā taha e rua.

$$9x^{2}+7-8=0$$

Tangohia te 8 i te 7, ka -1.

$$9x^{2}-1=0$$

Whakaarohia te 9x^{2}-1. Tuhia anō te 9x^{2}-1 hei \left(3x\right)^{2}-1^{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).

$$\left(3x-1\right)\left(3x+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te 3x-1=0 me te 3x+1=0.

$$x=\frac{1}{3} x=-\frac{1}{3}$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 7 mai i ngā taha e rua.

$$9x^{2}=8-7$$

Tangohia te 7 i te 8, ka 1.

$$9x^{2}=1$$

Whakawehea ngā taha e rua ki te 9.

$$x^{2}=\frac{1}{9}$$

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

$$x=\frac{1}{3} x=-\frac{1}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 8 mai i ngā taha e rua.

$$9x^{2}+7-8=0$$

Tangohia te 8 i te 7, ka -1.

$$9x^{2}-1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, 0 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-1\right)}}{2\times 9}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-1\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{0±\sqrt{-36\left(-1\right)}}{2\times 9}$$

Whakareatia -36 ki te -1.

$$x=\frac{0±\sqrt{36}}{2\times 9}$$

Tuhia te pūtakerua o te 36.

$$x=\frac{0±6}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{0±6}{18}$$

Nā, me whakaoti te whārite x=\frac{0±6}{18} ina he tāpiri te ±. Whakahekea te hautanga \frac{6}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x=\frac{1}{3}$$

Nā, me whakaoti te whārite x=\frac{0±6}{18} ina he tango te ±. Whakahekea te hautanga \frac{-6}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x=-\frac{1}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{3} x=-\frac{1}{3}$$