Whakaoti i te 1/2x^2+x-12=0

$$\frac { 1 } { 2 } x ^ { 2 } + x - 12 = 0$$

Whakaoti mō x

$$x=-6$$

$$x=4$$

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.

$$\frac{1}{2}x^{2}+x-12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{1}{2} mō a, 1 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\times \frac{1}{2}\left(-12\right)}}{2\times \frac{1}{2}}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\times \frac{1}{2}\left(-12\right)}}{2\times \frac{1}{2}}$$

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

$$x=\frac{-1±\sqrt{1-2\left(-12\right)}}{2\times \frac{1}{2}}$$

Whakareatia -2 ki te -12.

$$x=\frac{-1±\sqrt{1+24}}{2\times \frac{1}{2}}$$

Tāpiri 1 ki te 24.

$$x=\frac{-1±\sqrt{25}}{2\times \frac{1}{2}}$$

Tuhia te pūtakerua o te 25.

$$x=\frac{-1±5}{2\times \frac{1}{2}}$$

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

$$x=\frac{-1±5}{1}$$

Nā, me whakaoti te whārite x=\frac{-1±5}{1} ina he tāpiri te ±. Tāpiri -1 ki te 5.

$$x=\frac{4}{1}$$

Whakawehe 4 ki te 1.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{-1±5}{1} ina he tango te ±. Tango 5 mai i -1.

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

Whakawehe -6 ki te 1.

$$x=-6$$

Kua oti te whārite te whakatau.

$$x=4 x=-6$$

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.

$$\frac{1}{2}x^{2}+x-12=0$$

Me tāpiri 12 ki ngā taha e rua o te whārite.

$$\frac{1}{2}x^{2}+x-12-\left(-12\right)=-\left(-12\right)$$

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

$$\frac{1}{2}x^{2}+x=-\left(-12\right)$$

Tango -12 mai i 0.

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

Me whakarea ngā taha e rua ki te 2.

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

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

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

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

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

Whakawehe 12 ki te \frac{1}{2} mā te whakarea 12 ki te tau huripoki o \frac{1}{2}.

$$x^{2}+2x=24$$

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.

$$x^{2}+2x+1^{2}=24+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=24+1$$

Tāpiri 24 ki te 1.

$$x^{2}+2x+1=25$$

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}.

$$\left(x+1\right)^{2}=25$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{25}$$

Whakarūnātia.

$$x+1=5 x+1=-5$$

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

$$x=4 x=-6$$