Whakaoti i te 2x^2-35+180=0

$$2 x ^ { 2 } - 35 + 180 = 0$$

Whakaoti mō x (complex solution)

$$x=-\frac{\sqrt{290}i}{2}\approx -0-8.514693183i$$

$$x=\frac{\sqrt{290}i}{2}\approx 8.514693183i$$

Ngā Upane mā te Kimi Pūtakerua

Tāpirihia te -35 ki te 180, ka 145.

$$2x^{2}+145=0$$

Tangohia te 145 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2x^{2}=-145$$

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=-\frac{145}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{290}i}{2} x=-\frac{\sqrt{290}i}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te -35 ki te 180, ka 145.

$$2x^{2}+145=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me 145 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 145}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\times 145}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\times 145}}{2\times 2}$$

Whakareatia -8 ki te 145.

$$x=\frac{0±\sqrt{-1160}}{2\times 2}$$

Tuhia te pūtakerua o te -1160.

$$x=\frac{0±2\sqrt{290}i}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±2\sqrt{290}i}{4}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{290}i}{4} ina he tāpiri te ±.

$$x=\frac{\sqrt{290}i}{2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{290}i}{4} ina he tango te ±.

$$x=-\frac{\sqrt{290}i}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{290}i}{2} x=-\frac{\sqrt{290}i}{2}$$