Whakaoti i te 16x^2-8009+1000=0

$$16 x ^ { 2 } - 8009 + 1000 = 0$$

Whakaoti mō x

$$x = \frac{\sqrt{7009}}{4} \approx 20.929942666$$

$$x = -\frac{\sqrt{7009}}{4} \approx -20.929942666$$

Ngā Upane mā te Kimi Pūtakerua

Tāpirihia te -8009 ki te 1000, ka -7009.

$$16x^{2}-7009=0$$

Me tāpiri te 7009 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$16x^{2}=7009$$

Whakawehea ngā taha e rua ki te 16.

$$x^{2}=\frac{7009}{16}$$

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

$$x=\frac{\sqrt{7009}}{4} x=-\frac{\sqrt{7009}}{4}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te -8009 ki te 1000, ka -7009.

$$16x^{2}-7009=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 16 mō a, 0 mō b, me -7009 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-7009\right)}}{2\times 16}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-7009\right)}}{2\times 16}$$

Whakareatia -4 ki te 16.

$$x=\frac{0±\sqrt{-64\left(-7009\right)}}{2\times 16}$$

Whakareatia -64 ki te -7009.

$$x=\frac{0±\sqrt{448576}}{2\times 16}$$

Tuhia te pūtakerua o te 448576.

$$x=\frac{0±8\sqrt{7009}}{2\times 16}$$

Whakareatia 2 ki te 16.

$$x=\frac{0±8\sqrt{7009}}{32}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{7009}}{32} ina he tāpiri te ±.

$$x=\frac{\sqrt{7009}}{4}$$

Nā, me whakaoti te whārite x=\frac{0±8\sqrt{7009}}{32} ina he tango te ±.

$$x=-\frac{\sqrt{7009}}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{7009}}{4} x=-\frac{\sqrt{7009}}{4}$$