Whakaoti i te x^2-13x^2+40=0

$${ x }^{ 2 } -13 { x }^{ 2 } +40=0$$

Whakaoti mō x

$$x = \frac{\sqrt{30}}{3} \approx 1.825741858$$

$$x = -\frac{\sqrt{30}}{3} \approx -1.825741858$$

Ngā Upane mā te Kimi Pūtakerua

Pahekotia te x^{2} me -13x^{2}, ka -12x^{2}.

$$-12x^{2}+40=0$$

Tangohia te 40 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-12x^{2}=-40$$

Whakawehea ngā taha e rua ki te -12.

$$x^{2}=\frac{-40}{-12}$$

Whakahekea te hautanga \frac{-40}{-12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -4.

$$x^{2}=\frac{10}{3}$$

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

$$x=\frac{\sqrt{30}}{3} x=-\frac{\sqrt{30}}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te x^{2} me -13x^{2}, ka -12x^{2}.

$$-12x^{2}+40=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -12 mō a, 0 mō b, me 40 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-12\right)\times 40}}{2\left(-12\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-12\right)\times 40}}{2\left(-12\right)}$$

Whakareatia -4 ki te -12.

$$x=\frac{0±\sqrt{48\times 40}}{2\left(-12\right)}$$

Whakareatia 48 ki te 40.

$$x=\frac{0±\sqrt{1920}}{2\left(-12\right)}$$

Tuhia te pūtakerua o te 1920.

$$x=\frac{0±8\sqrt{30}}{2\left(-12\right)}$$

Whakareatia 2 ki te -12.

$$x=\frac{0±8\sqrt{30}}{-24}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{30}}{-24} ina he tāpiri te ±.

$$x=-\frac{\sqrt{30}}{3}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{30}}{-24} ina he tango te ±.

$$x=\frac{\sqrt{30}}{3}$$

Kua oti te whārite te whakatau.

$$x=-\frac{\sqrt{30}}{3} x=\frac{\sqrt{30}}{3}$$