Whakaoti i te 9x^2+18x+9=3

$$9 x ^ { 2 } + 18 x + 9 = 3$$

Whakaoti mō x

$$x=\frac{\sqrt{3}}{3}-1\approx -0.422649731$$

$$x=-\frac{\sqrt{3}}{3}-1\approx -1.577350269$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$9x^{2}+18x+9=3$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$9x^{2}+18x+9-3=3-3$$

Mā te tango i te 3 i a ia ake anō ka toe ko te 0.

$$9x^{2}+18x+9-3=0$$

Tango 3 mai i 9.

$$9x^{2}+18x+6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, 18 mō b, me 6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\times 9\times 6}}{2\times 9}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\times 9\times 6}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-18±\sqrt{324-36\times 6}}{2\times 9}$$

Whakareatia -36 ki te 6.

$$x=\frac{-18±\sqrt{324-216}}{2\times 9}$$

Tāpiri 324 ki te -216.

$$x=\frac{-18±\sqrt{108}}{2\times 9}$$

Tuhia te pūtakerua o te 108.

$$x=\frac{-18±6\sqrt{3}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{-18±6\sqrt{3}}{18}$$

Nā, me whakaoti te whārite x=\frac{-18±6\sqrt{3}}{18} ina he tāpiri te ±. Tāpiri -18 ki te 6\sqrt{3}.

$$x=\frac{6\sqrt{3}-18}{18}$$

Whakawehe -18+6\sqrt{3} ki te 18.

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

Nā, me whakaoti te whārite x=\frac{-18±6\sqrt{3}}{18} ina he tango te ±. Tango 6\sqrt{3} mai i -18.

$$x=\frac{-6\sqrt{3}-18}{18}$$

Whakawehe -18-6\sqrt{3} ki te 18.

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

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$9x^{2}+18x+9=3$$

Me tango 9 mai i ngā taha e rua o te whārite.

$$9x^{2}+18x+9-9=3-9$$

Mā te tango i te 9 i a ia ake anō ka toe ko te 0.

$$9x^{2}+18x=3-9$$

Tango 9 mai i 3.

$$9x^{2}+18x=-6$$

Whakawehea ngā taha e rua ki te 9.

$$\frac{9x^{2}+18x}{9}=-\frac{6}{9}$$

Mā te whakawehe ki te 9 ka wetekia te whakareanga ki te 9.

$$x^{2}+\frac{18}{9}x=-\frac{6}{9}$$

Whakawehe 18 ki te 9.

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

Whakahekea te hautanga \frac{-6}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

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

Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+2x+1^{2}=-\frac{2}{3}+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=-\frac{2}{3}+1$$

Tāpiri -\frac{2}{3} ki te 1.

$$x^{2}+2x+1=\frac{1}{3}$$

Tauwehea x^{2}+2x+1. 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}.

$$\left(x+1\right)^{2}=\frac{1}{3}$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{\frac{1}{3}}$$

Whakarūnātia.

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

Me tango 1 mai i ngā taha e rua o te whārite.

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