Whakaoti i te 4=20y^2+368y

$$4 = 20 y ^ { 2 } + 368 y$$

Whakaoti mō y

$$y=\frac{\sqrt{2121}-46}{5}\approx 0.010863152$$

$$y=\frac{-\sqrt{2121}-46}{5}\approx -18.410863152$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$20y^{2}+368y=4$$

Tangohia te 4 mai i ngā taha e rua.

$$20y^{2}+368y-4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 20 mō a, 368 mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-368±\sqrt{368^{2}-4\times 20\left(-4\right)}}{2\times 20}$$

Pūrua 368.

$$y=\frac{-368±\sqrt{135424-4\times 20\left(-4\right)}}{2\times 20}$$

Whakareatia -4 ki te 20.

$$y=\frac{-368±\sqrt{135424-80\left(-4\right)}}{2\times 20}$$

Whakareatia -80 ki te -4.

$$y=\frac{-368±\sqrt{135424+320}}{2\times 20}$$

Tāpiri 135424 ki te 320.

$$y=\frac{-368±\sqrt{135744}}{2\times 20}$$

Tuhia te pūtakerua o te 135744.

$$y=\frac{-368±8\sqrt{2121}}{2\times 20}$$

Whakareatia 2 ki te 20.

$$y=\frac{-368±8\sqrt{2121}}{40}$$

Nā, me whakaoti te whārite y=\frac{-368±8\sqrt{2121}}{40} ina he tāpiri te ±. Tāpiri -368 ki te 8\sqrt{2121}.

$$y=\frac{8\sqrt{2121}-368}{40}$$

Whakawehe -368+8\sqrt{2121} ki te 40.

$$y=\frac{\sqrt{2121}-46}{5}$$

Nā, me whakaoti te whārite y=\frac{-368±8\sqrt{2121}}{40} ina he tango te ±. Tango 8\sqrt{2121} mai i -368.

$$y=\frac{-8\sqrt{2121}-368}{40}$$

Whakawehe -368-8\sqrt{2121} ki te 40.

$$y=\frac{-\sqrt{2121}-46}{5}$$

Kua oti te whārite te whakatau.

$$y=\frac{\sqrt{2121}-46}{5} y=\frac{-\sqrt{2121}-46}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$20y^{2}+368y=4$$

Whakawehea ngā taha e rua ki te 20.

$$\frac{20y^{2}+368y}{20}=\frac{4}{20}$$

Mā te whakawehe ki te 20 ka wetekia te whakareanga ki te 20.

$$y^{2}+\frac{368}{20}y=\frac{4}{20}$$

Whakahekea te hautanga \frac{368}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$y^{2}+\frac{92}{5}y=\frac{4}{20}$$

Whakahekea te hautanga \frac{4}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$y^{2}+\frac{92}{5}y=\frac{1}{5}$$

Whakawehea te \frac{92}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{46}{5}. Nā, tāpiria te pūrua o te \frac{46}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$y^{2}+\frac{92}{5}y+\left(\frac{46}{5}\right)^{2}=\frac{1}{5}+\left(\frac{46}{5}\right)^{2}$$

Pūruatia \frac{46}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$y^{2}+\frac{92}{5}y+\frac{2116}{25}=\frac{1}{5}+\frac{2116}{25}$$

Tāpiri \frac{1}{5} ki te \frac{2116}{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.

$$y^{2}+\frac{92}{5}y+\frac{2116}{25}=\frac{2121}{25}$$

Tauwehea y^{2}+\frac{92}{5}y+\frac{2116}{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}.

$$\left(y+\frac{46}{5}\right)^{2}=\frac{2121}{25}$$

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

$$\sqrt{\left(y+\frac{46}{5}\right)^{2}}=\sqrt{\frac{2121}{25}}$$

Whakarūnātia.

$$y+\frac{46}{5}=\frac{\sqrt{2121}}{5} y+\frac{46}{5}=-\frac{\sqrt{2121}}{5}$$

Me tango \frac{46}{5} mai i ngā taha e rua o te whārite.

$$y=\frac{\sqrt{2121}-46}{5} y=\frac{-\sqrt{2121}-46}{5}$$