Whakaoti i te -x+1-x^2=1/4

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

Whakaoti mō x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$x=\frac{1}{2}=0.5$$

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.

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

Me tango \frac{1}{4} mai i ngā taha e rua o te whārite.

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

Mā te tango i te \frac{1}{4} i a ia ake anō ka toe ko te 0.

$$-x^{2}-x+1-\frac{1}{4}=0$$

Tango \frac{1}{4} mai i 1.

$$-x^{2}-x+\frac{3}{4}=0$$

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

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-1\right)\times \frac{3}{4}}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-1\right)±\sqrt{1+4\times \frac{3}{4}}}{2\left(-1\right)}$$

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

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

Tāpiri 1 ki te 3.

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

Tuhia te pūtakerua o te 4.

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

Ko te tauaro o -1 ko 1.

$$x=\frac{1±2}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{1±2}{-2}$$

Nā, me whakaoti te whārite x=\frac{1±2}{-2} ina he tāpiri te ±. Tāpiri 1 ki te 2.

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

Whakawehe 3 ki te -2.

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

Nā, me whakaoti te whārite x=\frac{1±2}{-2} ina he tango te ±. Tango 2 mai i 1.

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

Whakawehe -1 ki te -2.

$$x=\frac{1}{2}$$

Kua oti te whārite te whakatau.

$$x=-\frac{3}{2} x=\frac{1}{2}$$

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.

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

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

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

Mā te tango i te 1 i a ia ake anō ka toe ko te 0.

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

Tango 1 mai i \frac{1}{4}.

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

Whakawehea ngā taha e rua ki te -1.

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

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\left(-\frac{1}{-1}\right)x=-\frac{\frac{3}{4}}{-1}$$

Whakawehe -1 ki te -1.

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

Whakawehe -\frac{3}{4} ki te -1.

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

Whakawehea te 1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{2}. Nā, tāpiria te pūrua o te \frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=\frac{3}{4}+\left(\frac{1}{2}\right)^{2}$$

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

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

Tāpiri \frac{3}{4} ki te \frac{1}{4} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

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

Tauwehea x^{2}+x+\frac{1}{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}.

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

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

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

Whakarūnātia.

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

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{1}{2} x=-\frac{3}{2}$$