Whakaoti i te 0=2x^2+6x+2

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

Whakaoti mō x

$$x=\frac{\sqrt{5}-3}{2}\approx -0.381966011$$

$$x=\frac{-\sqrt{5}-3}{2}\approx -2.618033989$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

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

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

Pūrua 6.

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

Whakareatia -4 ki te 2.

$$x=\frac{-6±\sqrt{36-8\times 2}}{2\times 2}$$

Whakareatia -8 ki te 2.

$$x=\frac{-6±\sqrt{36-16}}{2\times 2}$$

Tāpiri 36 ki te -16.

$$x=\frac{-6±\sqrt{20}}{2\times 2}$$

Tuhia te pūtakerua o te 20.

$$x=\frac{-6±2\sqrt{5}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-6±2\sqrt{5}}{4}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{5}}{4} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{5}.

$$x=\frac{2\sqrt{5}-6}{4}$$

Whakawehe -6+2\sqrt{5} ki te 4.

$$x=\frac{\sqrt{5}-3}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{5}}{4} ina he tango te ±. Tango 2\sqrt{5} mai i -6.

$$x=\frac{-2\sqrt{5}-6}{4}$$

Whakawehe -6-2\sqrt{5} ki te 4.

$$x=\frac{-\sqrt{5}-3}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{5}-3}{2} x=\frac{-\sqrt{5}-3}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Whakawehea ngā taha e rua ki te 2.

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

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

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

Whakawehe 6 ki te 2.

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

Whakawehe -2 ki te 2.

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

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.

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

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

$$x^{2}+3x+\frac{9}{4}=-1+\frac{9}{4}$$

Tāpiri -1 ki te \frac{9}{4}.

$$x^{2}+3x+\frac{9}{4}=\frac{5}{4}$$

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}.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{5}{4}$$

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

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{5}{4}}$$

Whakarūnātia.

$$x+\frac{3}{2}=\frac{\sqrt{5}}{2} x+\frac{3}{2}=-\frac{\sqrt{5}}{2}$$

Me tango \frac{3}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{5}-3}{2} x=\frac{-\sqrt{5}-3}{2}$$