Whakaoti i te 1/2x^2+6x+18=0

$$\frac { 1 } { 2 } x ^ { 2 } + 6 x + 18 = 0$$

Whakaoti mō x

$$x=-6$$

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.

$$\frac{1}{2}x^{2}+6x+18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{1}{2} mō a, 6 mō b, me 18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\times \frac{1}{2}\times 18}}{2\times \frac{1}{2}}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\times \frac{1}{2}\times 18}}{2\times \frac{1}{2}}$$

Whakareatia -4 ki te \frac{1}{2}.

$$x=\frac{-6±\sqrt{36-2\times 18}}{2\times \frac{1}{2}}$$

Whakareatia -2 ki te 18.

$$x=\frac{-6±\sqrt{36-36}}{2\times \frac{1}{2}}$$

Tāpiri 36 ki te -36.

$$x=\frac{-6±\sqrt{0}}{2\times \frac{1}{2}}$$

Tuhia te pūtakerua o te 0.

$$x=-\frac{6}{2\times \frac{1}{2}}$$

Whakareatia 2 ki te \frac{1}{2}.

$$x=-\frac{6}{1}$$

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.

$$\frac{1}{2}x^{2}+6x+18=0$$

Me tango 18 mai i ngā taha e rua o te whārite.

$$\frac{1}{2}x^{2}+6x+18-18=-18$$

Mā te tango i te 18 i a ia ake anō ka toe ko te 0.

$$\frac{1}{2}x^{2}+6x=-18$$

Me whakarea ngā taha e rua ki te 2.

$$\frac{\frac{1}{2}x^{2}+6x}{\frac{1}{2}}=-\frac{18}{\frac{1}{2}}$$

Mā te whakawehe ki te \frac{1}{2} ka wetekia te whakareanga ki te \frac{1}{2}.

$$x^{2}+\frac{6}{\frac{1}{2}}x=-\frac{18}{\frac{1}{2}}$$

Whakawehe 6 ki te \frac{1}{2} mā te whakarea 6 ki te tau huripoki o \frac{1}{2}.

$$x^{2}+12x=-\frac{18}{\frac{1}{2}}$$

Whakawehe -18 ki te \frac{1}{2} mā te whakarea -18 ki te tau huripoki o \frac{1}{2}.

$$x^{2}+12x=-36$$

Whakawehea te 12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 6. Nā, tāpiria te pūrua o te 6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+12x+6^{2}=-36+6^{2}$$

Pūrua 6.

$$x^{2}+12x+36=-36+36$$

Tāpiri -36 ki te 36.

$$x^{2}+12x+36=0$$

Tauwehea x^{2}+12x+36. 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}.

$$\left(x+6\right)^{2}=0$$

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

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$x+6=0 x+6=0$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$x=-6 x=-6$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=-6$$