Whakaoti i te 100x^2-225=+11

$$100 x ^ { 2 } - 225 = + 11$$

Whakaoti mō x

$$x = \frac{\sqrt{59}}{5} \approx 1.53622915$$

$$x = -\frac{\sqrt{59}}{5} \approx -1.53622915$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 225 ki ngā taha e rua.

$$100x^{2}=11+225$$

Tāpirihia te 11 ki te 225, ka 236.

$$100x^{2}=236$$

Whakawehea ngā taha e rua ki te 100.

$$x^{2}=\frac{236}{100}$$

Whakahekea te hautanga \frac{236}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}=\frac{59}{25}$$

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

$$x=\frac{\sqrt{59}}{5} x=-\frac{\sqrt{59}}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 11 mai i ngā taha e rua.

$$100x^{2}-225-11=0$$

Tangohia te 11 i te -225, ka -236.

$$100x^{2}-236=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 100 mō a, 0 mō b, me -236 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 100\left(-236\right)}}{2\times 100}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 100\left(-236\right)}}{2\times 100}$$

Whakareatia -4 ki te 100.

$$x=\frac{0±\sqrt{-400\left(-236\right)}}{2\times 100}$$

Whakareatia -400 ki te -236.

$$x=\frac{0±\sqrt{94400}}{2\times 100}$$

Tuhia te pūtakerua o te 94400.

$$x=\frac{0±40\sqrt{59}}{2\times 100}$$

Whakareatia 2 ki te 100.

$$x=\frac{0±40\sqrt{59}}{200}$$

Nā, me whakaoti te whārite x=\frac{0±40\sqrt{59}}{200} ina he tāpiri te ±.

$$x=\frac{\sqrt{59}}{5}$$

Nā, me whakaoti te whārite x=\frac{0±40\sqrt{59}}{200} ina he tango te ±.

$$x=-\frac{\sqrt{59}}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{59}}{5} x=-\frac{\sqrt{59}}{5}$$