Whakaoti i te 16x^2+49=100

$$16 x ^ { 2 } + 49 = 100$$

Whakaoti mō x

$$x = \frac{\sqrt{51}}{4} \approx 1.785357107$$

$$x = -\frac{\sqrt{51}}{4} \approx -1.785357107$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 49 mai i ngā taha e rua.

$$16x^{2}=100-49$$

Tangohia te 49 i te 100, ka 51.

$$16x^{2}=51$$

Whakawehea ngā taha e rua ki te 16.

$$x^{2}=\frac{51}{16}$$

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

$$x=\frac{\sqrt{51}}{4} x=-\frac{\sqrt{51}}{4}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 100 mai i ngā taha e rua.

$$16x^{2}+49-100=0$$

Tangohia te 100 i te 49, ka -51.

$$16x^{2}-51=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 16 mō a, 0 mō b, me -51 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-51\right)}}{2\times 16}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-51\right)}}{2\times 16}$$

Whakareatia -4 ki te 16.

$$x=\frac{0±\sqrt{-64\left(-51\right)}}{2\times 16}$$

Whakareatia -64 ki te -51.

$$x=\frac{0±\sqrt{3264}}{2\times 16}$$

Tuhia te pūtakerua o te 3264.

$$x=\frac{0±8\sqrt{51}}{2\times 16}$$

Whakareatia 2 ki te 16.

$$x=\frac{0±8\sqrt{51}}{32}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{51}}{32} ina he tāpiri te ±.

$$x=\frac{\sqrt{51}}{4}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{51}}{32} ina he tango te ±.

$$x=-\frac{\sqrt{51}}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{51}}{4} x=-\frac{\sqrt{51}}{4}$$