Whakaoti i te 14x-7x^2=0x-2

$$14 x - 7 x ^ { 2 } = 0 x - 2$$

Whakaoti mō x

$$x=\frac{3\sqrt{7}}{7}+1\approx 2.133893419$$

$$x=-\frac{3\sqrt{7}}{7}+1\approx -0.133893419$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$14x-7x^{2}=0-2$$

Tangohia te 2 i te 0, ka -2.

$$14x-7x^{2}=-2$$

Me tāpiri te 2 ki ngā taha e rua.

$$14x-7x^{2}+2=0$$

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.

$$-7x^{2}+14x+2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -7 mō a, 14 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-14±\sqrt{14^{2}-4\left(-7\right)\times 2}}{2\left(-7\right)}$$

Pūrua 14.

$$x=\frac{-14±\sqrt{196-4\left(-7\right)\times 2}}{2\left(-7\right)}$$

Whakareatia -4 ki te -7.

$$x=\frac{-14±\sqrt{196+28\times 2}}{2\left(-7\right)}$$

Whakareatia 28 ki te 2.

$$x=\frac{-14±\sqrt{196+56}}{2\left(-7\right)}$$

Tāpiri 196 ki te 56.

$$x=\frac{-14±\sqrt{252}}{2\left(-7\right)}$$

Tuhia te pūtakerua o te 252.

$$x=\frac{-14±6\sqrt{7}}{2\left(-7\right)}$$

Whakareatia 2 ki te -7.

$$x=\frac{-14±6\sqrt{7}}{-14}$$

Nā, me whakaoti te whārite x=\frac{-14±6\sqrt{7}}{-14} ina he tāpiri te ±. Tāpiri -14 ki te 6\sqrt{7}.

$$x=\frac{6\sqrt{7}-14}{-14}$$

Whakawehe -14+6\sqrt{7} ki te -14.

$$x=-\frac{3\sqrt{7}}{7}+1$$

Nā, me whakaoti te whārite x=\frac{-14±6\sqrt{7}}{-14} ina he tango te ±. Tango 6\sqrt{7} mai i -14.

$$x=\frac{-6\sqrt{7}-14}{-14}$$

Whakawehe -14-6\sqrt{7} ki te -14.

$$x=\frac{3\sqrt{7}}{7}+1$$

Kua oti te whārite te whakatau.

$$x=-\frac{3\sqrt{7}}{7}+1 x=\frac{3\sqrt{7}}{7}+1$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$14x-7x^{2}=0-2$$

Tangohia te 2 i te 0, ka -2.

$$14x-7x^{2}=-2$$

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.

$$-7x^{2}+14x=-2$$

Whakawehea ngā taha e rua ki te -7.

$$\frac{-7x^{2}+14x}{-7}=-\frac{2}{-7}$$

Mā te whakawehe ki te -7 ka wetekia te whakareanga ki te -7.

$$x^{2}+\frac{14}{-7}x=-\frac{2}{-7}$$

Whakawehe 14 ki te -7.

$$x^{2}-2x=-\frac{2}{-7}$$

Whakawehe -2 ki te -7.

$$x^{2}-2x=\frac{2}{7}$$

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.

$$x^{2}-2x+1=\frac{2}{7}+1$$

Tāpiri \frac{2}{7} ki te 1.

$$x^{2}-2x+1=\frac{9}{7}$$

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}.

$$\left(x-1\right)^{2}=\frac{9}{7}$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{9}{7}}$$

Whakarūnātia.

$$x-1=\frac{3\sqrt{7}}{7} x-1=-\frac{3\sqrt{7}}{7}$$

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

$$x=\frac{3\sqrt{7}}{7}+1 x=-\frac{3\sqrt{7}}{7}+1$$