Whakaoti i te x^2+6x+9=12

$$x ^ { 2 } + 6 x + 9 = 12$$

Whakaoti mō x

$$x=2\sqrt{3}-3\approx 0.464101615$$

$$x=-2\sqrt{3}-3\approx -6.464101615$$

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.

$$x^{2}+6x+9=12$$

Me tango 12 mai i ngā taha e rua o te whārite.

$$x^{2}+6x+9-12=12-12$$

Mā te tango i te 12 i a ia ake anō ka toe ko te 0.

$$x^{2}+6x+9-12=0$$

Tango 12 mai i 9.

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

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

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

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\left(-3\right)}}{2}$$

Whakareatia -4 ki te -3.

$$x=\frac{-6±\sqrt{36+12}}{2}$$

Tāpiri 36 ki te 12.

$$x=\frac{-6±\sqrt{48}}{2}$$

Tuhia te pūtakerua o te 48.

$$x=\frac{-6±4\sqrt{3}}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±4\sqrt{3}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 4\sqrt{3}.

$$x=\frac{4\sqrt{3}-6}{2}$$

Whakawehe -6+4\sqrt{3} ki te 2.

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

Nā, me whakaoti te whārite x=\frac{-6±4\sqrt{3}}{2} ina he tango te ±. Tango 4\sqrt{3} mai i -6.

$$x=\frac{-4\sqrt{3}-6}{2}$$

Whakawehe -6-4\sqrt{3} ki te 2.

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

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Tauwehea x^{2}+6x+9. 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}.

$$\left(x+3\right)^{2}=12$$

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

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{12}$$

Whakarūnātia.

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

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

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