Whakaoti i te 4x^2+4x+1=9x^2

$$4 x ^ { 2 } + 4 x + 1 = 9 x ^ { 2 }$$

Whakaoti mō x

$$x=-\frac{1}{5}=-0.2$$

$$x=1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 9x^{2} mai i ngā taha e rua.

$$4x^{2}+4x+1-9x^{2}=0$$

Pahekotia te 4x^{2} me -9x^{2}, ka -5x^{2}.

$$-5x^{2}+4x+1=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -5x^{2}+ax+bx+1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=4 ab=-5=-5$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=5 b=-1$$

Tuhia anō te -5x^{2}+4x+1 hei \left(-5x^{2}+5x\right)+\left(-x+1\right).

$$\left(-5x^{2}+5x\right)+\left(-x+1\right)$$

Whakatauwehea atu 5x i te -5x^{2}+5x.

$$5x\left(-x+1\right)-x+1$$

Whakatauwehea atu te kīanga pātahi -x+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-x+1\right)\left(5x+1\right)$$

Hei kimi otinga whārite, me whakaoti te -x+1=0 me te 5x+1=0.

$$x=1 x=-\frac{1}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 9x^{2} mai i ngā taha e rua.

$$4x^{2}+4x+1-9x^{2}=0$$

Pahekotia te 4x^{2} me -9x^{2}, ka -5x^{2}.

$$-5x^{2}+4x+1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -5 mō a, 4 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\left(-5\right)}}{2\left(-5\right)}$$

Whakareatia -4 ki te -5.

$$x=\frac{-4±\sqrt{16+20}}{2\left(-5\right)}$$

Tāpiri 16 ki te 20.

$$x=\frac{-4±\sqrt{36}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te 36.

$$x=\frac{-4±6}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$x=\frac{-4±6}{-10}$$

Nā, me whakaoti te whārite x=\frac{-4±6}{-10} ina he tāpiri te ±. Tāpiri -4 ki te 6.

$$x=\frac{2}{-10}$$

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

$$x=-\frac{1}{5}$$

Nā, me whakaoti te whārite x=\frac{-4±6}{-10} ina he tango te ±. Tango 6 mai i -4.

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

Whakawehe -10 ki te -10.

$$x=1$$

Kua oti te whārite te whakatau.

$$x=-\frac{1}{5} x=1$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 9x^{2} mai i ngā taha e rua.

$$4x^{2}+4x+1-9x^{2}=0$$

Pahekotia te 4x^{2} me -9x^{2}, ka -5x^{2}.

$$-5x^{2}+4x+1=0$$

Tangohia te 1 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-5x^{2}+4x=-1$$

Whakawehea ngā taha e rua ki te -5.

$$\frac{-5x^{2}+4x}{-5}=-\frac{1}{-5}$$

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

$$x^{2}+\frac{4}{-5}x=-\frac{1}{-5}$$

Whakawehe 4 ki te -5.

$$x^{2}-\frac{4}{5}x=-\frac{1}{-5}$$

Whakawehe -1 ki te -5.

$$x^{2}-\frac{4}{5}x=\frac{1}{5}$$

Whakawehea te -\frac{4}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{2}{5}. Nā, tāpiria te pūrua o te -\frac{2}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{4}{5}x+\left(-\frac{2}{5}\right)^{2}=\frac{1}{5}+\left(-\frac{2}{5}\right)^{2}$$

Pūruatia -\frac{2}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{4}{5}x+\frac{4}{25}=\frac{1}{5}+\frac{4}{25}$$

Tāpiri \frac{1}{5} ki te \frac{4}{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.

$$x^{2}-\frac{4}{5}x+\frac{4}{25}=\frac{9}{25}$$

Tauwehea x^{2}-\frac{4}{5}x+\frac{4}{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}.

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

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

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

Whakarūnātia.

$$x-\frac{2}{5}=\frac{3}{5} x-\frac{2}{5}=-\frac{3}{5}$$

Me tāpiri \frac{2}{5} ki ngā taha e rua o te whārite.

$$x=1 x=-\frac{1}{5}$$