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

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

Whakaoti mō x (complex solution)

$$x=-\frac{\sqrt{14}i}{2}\approx -0-1.870828693i$$

$$x=\frac{\sqrt{14}i}{2}\approx 1.870828693i$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia ngā taha e rua o te whārite ki te 2.

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

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te \frac{1}{2} mai i ngā taha e rua.

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

Tangohia te \frac{1}{2} i te 4, ka \frac{7}{2}.

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

Whakawehea ngā taha e rua ki te -1.

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

Tuhia te \frac{\frac{7}{2}}{-1} hei hautanga kotahi.

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

Whakareatia te 2 ki te -1, ka -2.

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

Ka taea te hautanga \frac{7}{-2} te tuhi anō ko -\frac{7}{2} mā te tango i te tohu tōraro.

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

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{14}i}{2} x=-\frac{\sqrt{14}i}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

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

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te 4 mai i ngā taha e rua.

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

Tangohia te 4 i te \frac{1}{2}, ka -\frac{7}{2}.

$$-x^{2}-\frac{7}{2}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 0 mō b, me -\frac{7}{2} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-\frac{7}{2}\right)}}{2\left(-1\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-\frac{7}{2}\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{0±\sqrt{4\left(-\frac{7}{2}\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -\frac{7}{2}.

$$x=\frac{0±\sqrt{-14}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te -14.

$$x=\frac{0±\sqrt{14}i}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{0±\sqrt{14}i}{-2}$$

Nā, me whakaoti te whārite x=\frac{0±\sqrt{14}i}{-2} ina he tāpiri te ±.

$$x=-\frac{\sqrt{14}i}{2}$$

Nā, me whakaoti te whārite x=\frac{0±\sqrt{14}i}{-2} ina he tango te ±.

$$x=\frac{\sqrt{14}i}{2}$$

Kua oti te whārite te whakatau.

$$x=-\frac{\sqrt{14}i}{2} x=\frac{\sqrt{14}i}{2}$$