Whakaoti i te 8x^2+9=313

$$8 x ^ { 2 } + 9 = 313$$

Whakaoti mō x

$$x=\sqrt{38}\approx 6.164414003$$

$$x=-\sqrt{38}\approx -6.164414003$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 9 mai i ngā taha e rua.

$$8x^{2}=313-9$$

Tangohia te 9 i te 313, ka 304.

$$8x^{2}=304$$

Whakawehea ngā taha e rua ki te 8.

$$x^{2}=\frac{304}{8}$$

Whakawehea te 304 ki te 8, kia riro ko 38.

$$x^{2}=38$$

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

$$x=\sqrt{38} x=-\sqrt{38}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 313 mai i ngā taha e rua.

$$8x^{2}+9-313=0$$

Tangohia te 313 i te 9, ka -304.

$$8x^{2}-304=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, 0 mō b, me -304 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-304\right)}}{2\times 8}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-304\right)}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$x=\frac{0±\sqrt{-32\left(-304\right)}}{2\times 8}$$

Whakareatia -32 ki te -304.

$$x=\frac{0±\sqrt{9728}}{2\times 8}$$

Tuhia te pūtakerua o te 9728.

$$x=\frac{0±16\sqrt{38}}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{0±16\sqrt{38}}{16}$$

Nā, me whakaoti te whārite x=\frac{0±16\sqrt{38}}{16} ina he tāpiri te ±.

$$x=\sqrt{38}$$

Nā, me whakaoti te whārite x=\frac{0±16\sqrt{38}}{16} ina he tango te ±.

$$x=-\sqrt{38}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{38} x=-\sqrt{38}$$