Whakaoti i te x^2+2x-3/2=0

$${ x }^{ 2 } +2x- \frac{ 3 }{ 2 } =0$$

Whakaoti mō x

$$x=\frac{\sqrt{10}}{2}-1\approx 0.58113883$$

$$x=-\frac{\sqrt{10}}{2}-1\approx -2.58113883$$

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.

$$x^{2}+2x-\frac{3}{2}=0$$

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

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

Pūrua 2.

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

Whakareatia -4 ki te -\frac{3}{2}.

$$x=\frac{-2±\sqrt{4+6}}{2}$$

Tāpiri 4 ki te 6.

$$x=\frac{-2±\sqrt{10}}{2}$$

Nā, me whakaoti te whārite x=\frac{-2±\sqrt{10}}{2} ina he tāpiri te ±. Tāpiri -2 ki te \sqrt{10}.

$$x=\frac{\sqrt{10}-2}{2}$$

Whakawehe -2+\sqrt{10} ki te 2.

$$x=\frac{\sqrt{10}}{2}-1$$

Nā, me whakaoti te whārite x=\frac{-2±\sqrt{10}}{2} ina he tango te ±. Tango \sqrt{10} mai i -2.

$$x=\frac{-\sqrt{10}-2}{2}$$

Whakawehe -2-\sqrt{10} ki te 2.

$$x=-\frac{\sqrt{10}}{2}-1$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{10}}{2}-1 x=-\frac{\sqrt{10}}{2}-1$$

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.

$$x^{2}+2x-\frac{3}{2}=0$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

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

Mā te tango i te -\frac{3}{2} i a ia ake anō ka toe ko te 0.

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

Tango -\frac{3}{2} mai i 0.

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

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.

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

Pūrua 1.

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

Tāpiri \frac{3}{2} ki te 1.

$$x^{2}+2x+1=\frac{5}{2}$$

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}.

$$\left(x+1\right)^{2}=\frac{5}{2}$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{\frac{5}{2}}$$

Whakarūnātia.

$$x+1=\frac{\sqrt{10}}{2} x+1=-\frac{\sqrt{10}}{2}$$

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

$$x=\frac{\sqrt{10}}{2}-1 x=-\frac{\sqrt{10}}{2}-1$$