Whakaoti i te -8=5x^2-14x

$$- 8 = 5 x ^ { 2 } - 14 x$$

Whakaoti mō x

$$x=2$$

$$x=\frac{4}{5}=0.8$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$5x^{2}-14x=-8$$

Me tāpiri te 8 ki ngā taha e rua.

$$5x^{2}-14x+8=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 5x^{2}+ax+bx+8. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-14 ab=5\times 8=40$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 40.

$$-1,-40 -2,-20 -4,-10 -5,-8$$

Tātaihia te tapeke mō ia takirua.

$$-1-40=-41 -2-20=-22 -4-10=-14 -5-8=-13$$

Ko te otinga te takirua ka hoatu i te tapeke -14.

$$a=-10 b=-4$$

Tuhia anō te 5x^{2}-14x+8 hei \left(5x^{2}-10x\right)+\left(-4x+8\right).

$$\left(5x^{2}-10x\right)+\left(-4x+8\right)$$

Tauwehea te 5x i te tuatahi me te -4 i te rōpū tuarua.

$$5x\left(x-2\right)-4\left(x-2\right)$$

Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-2\right)\left(5x-4\right)$$

Hei kimi otinga whārite, me whakaoti te x-2=0 me te 5x-4=0.

$$x=2 x=\frac{4}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$5x^{2}-14x=-8$$

Me tāpiri te 8 ki ngā taha e rua.

$$5x^{2}-14x+8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -14 mō b, me 8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 5\times 8}}{2\times 5}$$

Pūrua -14.

$$x=\frac{-\left(-14\right)±\sqrt{196-4\times 5\times 8}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-14\right)±\sqrt{196-20\times 8}}{2\times 5}$$

Whakareatia -20 ki te 8.

$$x=\frac{-\left(-14\right)±\sqrt{196-160}}{2\times 5}$$

Tāpiri 196 ki te -160.

$$x=\frac{-\left(-14\right)±\sqrt{36}}{2\times 5}$$

Tuhia te pūtakerua o te 36.

$$x=\frac{-\left(-14\right)±6}{2\times 5}$$

Ko te tauaro o -14 ko 14.

$$x=\frac{14±6}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{14±6}{10}$$

Nā, me whakaoti te whārite x=\frac{14±6}{10} ina he tāpiri te ±. Tāpiri 14 ki te 6.

$$x=\frac{20}{10}$$

Whakawehe 20 ki te 10.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{14±6}{10} ina he tango te ±. Tango 6 mai i 14.

$$x=\frac{8}{10}$$

Whakahekea te hautanga \frac{8}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{4}{5}$$

Kua oti te whārite te whakatau.

$$x=2 x=\frac{4}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$5x^{2}-14x=-8$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}-14x}{5}=-\frac{8}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$x^{2}-\frac{14}{5}x=-\frac{8}{5}$$

Whakawehea te -\frac{14}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{5}. Nā, tāpiria te pūrua o te -\frac{7}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{14}{5}x+\left(-\frac{7}{5}\right)^{2}=-\frac{8}{5}+\left(-\frac{7}{5}\right)^{2}$$

Pūruatia -\frac{7}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{14}{5}x+\frac{49}{25}=-\frac{8}{5}+\frac{49}{25}$$

Tāpiri -\frac{8}{5} ki te \frac{49}{25} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{14}{5}x+\frac{49}{25}=\frac{9}{25}$$

Tauwehea x^{2}-\frac{14}{5}x+\frac{49}{25}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{5}\right)^{2}=\frac{9}{25}$$

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

$$\sqrt{\left(x-\frac{7}{5}\right)^{2}}=\sqrt{\frac{9}{25}}$$

Whakarūnātia.

$$x-\frac{7}{5}=\frac{3}{5} x-\frac{7}{5}=-\frac{3}{5}$$

Me tāpiri \frac{7}{5} ki ngā taha e rua o te whārite.

$$x=2 x=\frac{4}{5}$$