Whakaoti i te (x+2)(x-2)=3x+2

$$( x + 2 ) ( x - 2 ) = 3 x + 2$$

Whakaoti mō x

$$x = \frac{\sqrt{33} + 3}{2} \approx 4.372281323$$

$$x=\frac{3-\sqrt{33}}{2}\approx -1.372281323$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakaarohia te \left(x+2\right)\left(x-2\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 2.

$$x^{2}-4=3x+2$$

Tangohia te 3x mai i ngā taha e rua.

$$x^{2}-4-3x=2$$

Tangohia te 2 mai i ngā taha e rua.

$$x^{2}-4-3x-2=0$$

Tangohia te 2 i te -4, ka -6.

$$x^{2}-6-3x=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x^{2}-3x-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -3 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-6\right)}}{2}$$

Pūrua -3.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-6\right)}}{2}$$

Whakareatia -4 ki te -6.

$$x=\frac{-\left(-3\right)±\sqrt{9+24}}{2}$$

Tāpiri 9 ki te 24.

$$x=\frac{-\left(-3\right)±\sqrt{33}}{2}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±\sqrt{33}}{2}$$

Nā, me whakaoti te whārite x=\frac{3±\sqrt{33}}{2} ina he tāpiri te ±. Tāpiri 3 ki te \sqrt{33}.

$$x=\frac{\sqrt{33}+3}{2}$$

Nā, me whakaoti te whārite x=\frac{3±\sqrt{33}}{2} ina he tango te ±. Tango \sqrt{33} mai i 3.

$$x=\frac{3-\sqrt{33}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{33}+3}{2} x=\frac{3-\sqrt{33}}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakaarohia te \left(x+2\right)\left(x-2\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 2.

$$x^{2}-4=3x+2$$

Tangohia te 3x mai i ngā taha e rua.

$$x^{2}-4-3x=2$$

Me tāpiri te 4 ki ngā taha e rua.

$$x^{2}-3x=2+4$$

Tāpirihia te 2 ki te 4, ka 6.

$$x^{2}-3x=6$$

Whakawehea te -3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{2}. Nā, tāpiria te pūrua o te -\frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=6+\left(-\frac{3}{2}\right)^{2}$$

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3x+\frac{9}{4}=6+\frac{9}{4}$$

Tāpiri 6 ki te \frac{9}{4}.

$$x^{2}-3x+\frac{9}{4}=\frac{33}{4}$$

Tauwehea x^{2}-3x+\frac{9}{4}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{33}{4}$$

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

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{33}{4}}$$

Whakarūnātia.

$$x-\frac{3}{2}=\frac{\sqrt{33}}{2} x-\frac{3}{2}=-\frac{\sqrt{33}}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{33}+3}{2} x=\frac{3-\sqrt{33}}{2}$$