Whakaoti i te -1/2x^2-3/2x+2=2

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

Whakaoti mō x

$$x=-3$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 2 mai i ngā taha e rua.

$$-\frac{1}{2}x^{2}-\frac{3}{2}x+2-2=0$$

Tangohia te 2 i te 2, ka 0.

$$-\frac{1}{2}x^{2}-\frac{3}{2}x=0$$

Tauwehea te x.

$$x\left(-\frac{1}{2}x-\frac{3}{2}\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te \frac{-x-3}{2}=0.

$$x=0 x=-3$$

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.

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

Me tango 2 mai i ngā taha e rua o te whārite.

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

Mā te tango i te 2 i a ia ake anō ka toe ko te 0.

$$-\frac{1}{2}x^{2}-\frac{3}{2}x+2-2=0$$

Tango 2 mai i 2.

$$-\frac{1}{2}x^{2}-\frac{3}{2}x=0$$

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

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

Tuhia te pūtakerua o te \left(-\frac{3}{2}\right)^{2}.

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

Ko te tauaro o -\frac{3}{2} ko \frac{3}{2}.

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

Whakareatia 2 ki te -\frac{1}{2}.

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

Nā, me whakaoti te whārite x=\frac{\frac{3}{2}±\frac{3}{2}}{-1} ina he tāpiri te ±. Tāpiri \frac{3}{2} ki te \frac{3}{2} 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.

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

Whakawehe 3 ki te -1.

$$x=-3$$

Nā, me whakaoti te whārite x=\frac{\frac{3}{2}±\frac{3}{2}}{-1} ina he tango te ±. Tango \frac{3}{2} mai i \frac{3}{2} mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-3 x=0$$

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.

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

Me tango 2 mai i ngā taha e rua o te whārite.

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

Mā te tango i te 2 i a ia ake anō ka toe ko te 0.

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

Tango 2 mai i 2.

$$-\frac{1}{2}x^{2}-\frac{3}{2}x=0$$

Me whakarea ngā taha e rua ki te -2.

$$\frac{-\frac{1}{2}x^{2}-\frac{3}{2}x}{-\frac{1}{2}}=\frac{0}{-\frac{1}{2}}$$

Mā te whakawehe ki te -\frac{1}{2} ka wetekia te whakareanga ki te -\frac{1}{2}.

$$x^{2}+\left(-\frac{\frac{3}{2}}{-\frac{1}{2}}\right)x=\frac{0}{-\frac{1}{2}}$$

Whakawehe -\frac{3}{2} ki te -\frac{1}{2} mā te whakarea -\frac{3}{2} ki te tau huripoki o -\frac{1}{2}.

$$x^{2}+3x=\frac{0}{-\frac{1}{2}}$$

Whakawehe 0 ki te -\frac{1}{2} mā te whakarea 0 ki te tau huripoki o -\frac{1}{2}.

$$x^{2}+3x=0$$

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.

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

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

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

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}.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

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

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

$$x=0 x=-3$$