Whakaoti i te x^2-2x+28/37=0

$${ x }^{ 2 } -2x+ \frac{ 28 }{ 37 } =0$$

Whakaoti mō x

$$x=\frac{3\sqrt{37}}{37}+1\approx 1.493196962$$

$$x=-\frac{3\sqrt{37}}{37}+1\approx 0.506803038$$

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.

$$x^{2}-2x+\frac{28}{37}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me \frac{28}{37} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times \frac{28}{37}}}{2}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times \frac{28}{37}}}{2}$$

Whakareatia -4 ki te \frac{28}{37}.

$$x=\frac{-\left(-2\right)±\sqrt{4-\frac{112}{37}}}{2}$$

Tāpiri 4 ki te -\frac{112}{37}.

$$x=\frac{-\left(-2\right)±\sqrt{\frac{36}{37}}}{2}$$

Tuhia te pūtakerua o te \frac{36}{37}.

$$x=\frac{-\left(-2\right)±\frac{6\sqrt{37}}{37}}{2}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±\frac{6\sqrt{37}}{37}}{2}$$

Nā, me whakaoti te whārite x=\frac{2±\frac{6\sqrt{37}}{37}}{2} ina he tāpiri te ±. Tāpiri 2 ki te \frac{6\sqrt{37}}{37}.

$$x=\frac{\frac{6\sqrt{37}}{37}+2}{2}$$

Whakawehe 2+\frac{6\sqrt{37}}{37} ki te 2.

$$x=\frac{3\sqrt{37}}{37}+1$$

Nā, me whakaoti te whārite x=\frac{2±\frac{6\sqrt{37}}{37}}{2} ina he tango te ±. Tango \frac{6\sqrt{37}}{37} mai i 2.

$$x=\frac{-\frac{6\sqrt{37}}{37}+2}{2}$$

Whakawehe 2-\frac{6\sqrt{37}}{37} ki te 2.

$$x=-\frac{3\sqrt{37}}{37}+1$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{37}}{37}+1 x=-\frac{3\sqrt{37}}{37}+1$$

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.

$$x^{2}-2x+\frac{28}{37}=0$$

Me tango \frac{28}{37} mai i ngā taha e rua o te whārite.

$$x^{2}-2x+\frac{28}{37}-\frac{28}{37}=-\frac{28}{37}$$

Mā te tango i te \frac{28}{37} i a ia ake anō ka toe ko te 0.

$$x^{2}-2x=-\frac{28}{37}$$

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.

$$x^{2}-2x+1=-\frac{28}{37}+1$$

Tāpiri -\frac{28}{37} ki te 1.

$$x^{2}-2x+1=\frac{9}{37}$$

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}.

$$\left(x-1\right)^{2}=\frac{9}{37}$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{9}{37}}$$

Whakarūnātia.

$$x-1=\frac{3\sqrt{37}}{37} x-1=-\frac{3\sqrt{37}}{37}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{37}}{37}+1 x=-\frac{3\sqrt{37}}{37}+1$$