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

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

Whakaoti mō x

$$x=-4$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x, arā, te tauraro pātahi he tino iti rawa te kitea o x,2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te -\frac{1}{2}x^{2}-\frac{3}{2}x.

$$-x^{2}-3x=x$$

Tangohia te x mai i ngā taha e rua.

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

Pahekotia te -3x me -x, ka -4x.

$$-x^{2}-4x=0$$

Tauwehea te x.

$$x\left(-x-4\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -x-4=0.

$$x=0 x=-4$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x, arā, te tauraro pātahi he tino iti rawa te kitea o x,2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te -\frac{1}{2}x^{2}-\frac{3}{2}x.

$$-x^{2}-3x=x$$

Tangohia te x mai i ngā taha e rua.

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

Pahekotia te -3x me -x, ka -4x.

$$-x^{2}-4x=0$$

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

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

Tuhia te pūtakerua o te \left(-4\right)^{2}.

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

Ko te tauaro o -4 ko 4.

$$x=\frac{4±4}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{4±4}{-2}$$

Nā, me whakaoti te whārite x=\frac{4±4}{-2} ina he tāpiri te ±. Tāpiri 4 ki te 4.

$$x=\frac{8}{-2}$$

Whakawehe 8 ki te -2.

$$x=-4$$

Nā, me whakaoti te whārite x=\frac{4±4}{-2} ina he tango te ±. Tango 4 mai i 4.

$$x=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-4 x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-4$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2x, arā, te tauraro pātahi he tino iti rawa te kitea o x,2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te -\frac{1}{2}x^{2}-\frac{3}{2}x.

$$-x^{2}-3x=x$$

Tangohia te x mai i ngā taha e rua.

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

Pahekotia te -3x me -x, ka -4x.

$$-x^{2}-4x=0$$

Whakawehea ngā taha e rua ki te -1.

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

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

$$x^{2}+\left(-\frac{4}{-1}\right)x=\frac{0}{-1}$$

Whakawehe -4 ki te -1.

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

Whakawehe 0 ki te -1.

$$x^{2}+4x=0$$

Whakawehea te 4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 2. Nā, tāpiria te pūrua o te 2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+4x+2^{2}=2^{2}$$

Pūrua 2.

$$x^{2}+4x+4=4$$

Tauwehea x^{2}+4x+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}.

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

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

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

Whakarūnātia.

$$x+2=2 x+2=-2$$

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

$$x=0 x=-4$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-4$$