Whakaoti i te x+4/5xx=300-39

$$x + \frac { 4 } { 5 } x x = 300 - 39$$

Whakaoti mō x

$$x = \frac{\sqrt{20905} - 5}{8} \approx 17.448201847$$

$$x=\frac{-\sqrt{20905}-5}{8}\approx -18.698201847$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te x ki te x, ka x^{2}.

$$x+\frac{4}{5}x^{2}=300-39$$

Tangohia te 39 i te 300, ka 261.

$$x+\frac{4}{5}x^{2}=261$$

Tangohia te 261 mai i ngā taha e rua.

$$x+\frac{4}{5}x^{2}-261=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$\frac{4}{5}x^{2}+x-261=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{4}{5} mō a, 1 mō b, me -261 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\times \frac{4}{5}\left(-261\right)}}{2\times \frac{4}{5}}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\times \frac{4}{5}\left(-261\right)}}{2\times \frac{4}{5}}$$

Whakareatia -4 ki te \frac{4}{5}.

$$x=\frac{-1±\sqrt{1-\frac{16}{5}\left(-261\right)}}{2\times \frac{4}{5}}$$

Whakareatia -\frac{16}{5} ki te -261.

$$x=\frac{-1±\sqrt{1+\frac{4176}{5}}}{2\times \frac{4}{5}}$$

Tāpiri 1 ki te \frac{4176}{5}.

$$x=\frac{-1±\sqrt{\frac{4181}{5}}}{2\times \frac{4}{5}}$$

Tuhia te pūtakerua o te \frac{4181}{5}.

$$x=\frac{-1±\frac{\sqrt{20905}}{5}}{2\times \frac{4}{5}}$$

Whakareatia 2 ki te \frac{4}{5}.

$$x=\frac{-1±\frac{\sqrt{20905}}{5}}{\frac{8}{5}}$$

Nā, me whakaoti te whārite x=\frac{-1±\frac{\sqrt{20905}}{5}}{\frac{8}{5}} ina he tāpiri te ±. Tāpiri -1 ki te \frac{\sqrt{20905}}{5}.

$$x=\frac{\frac{\sqrt{20905}}{5}-1}{\frac{8}{5}}$$

Whakawehe -1+\frac{\sqrt{20905}}{5} ki te \frac{8}{5} mā te whakarea -1+\frac{\sqrt{20905}}{5} ki te tau huripoki o \frac{8}{5}.

$$x=\frac{\sqrt{20905}-5}{8}$$

Nā, me whakaoti te whārite x=\frac{-1±\frac{\sqrt{20905}}{5}}{\frac{8}{5}} ina he tango te ±. Tango \frac{\sqrt{20905}}{5} mai i -1.

$$x=\frac{-\frac{\sqrt{20905}}{5}-1}{\frac{8}{5}}$$

Whakawehe -1-\frac{\sqrt{20905}}{5} ki te \frac{8}{5} mā te whakarea -1-\frac{\sqrt{20905}}{5} ki te tau huripoki o \frac{8}{5}.

$$x=\frac{-\sqrt{20905}-5}{8}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{20905}-5}{8} x=\frac{-\sqrt{20905}-5}{8}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te x ki te x, ka x^{2}.

$$x+\frac{4}{5}x^{2}=300-39$$

Tangohia te 39 i te 300, ka 261.

$$x+\frac{4}{5}x^{2}=261$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$\frac{4}{5}x^{2}+x=261$$

Whakawehea ngā taha e rua o te whārite ki te \frac{4}{5}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{\frac{4}{5}x^{2}+x}{\frac{4}{5}}=\frac{261}{\frac{4}{5}}$$

Mā te whakawehe ki te \frac{4}{5} ka wetekia te whakareanga ki te \frac{4}{5}.

$$x^{2}+\frac{1}{\frac{4}{5}}x=\frac{261}{\frac{4}{5}}$$

Whakawehe 1 ki te \frac{4}{5} mā te whakarea 1 ki te tau huripoki o \frac{4}{5}.

$$x^{2}+\frac{5}{4}x=\frac{261}{\frac{4}{5}}$$

Whakawehe 261 ki te \frac{4}{5} mā te whakarea 261 ki te tau huripoki o \frac{4}{5}.

$$x^{2}+\frac{5}{4}x=\frac{1305}{4}$$

Whakawehea te \frac{5}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{8}. Nā, tāpiria te pūrua o te \frac{5}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{5}{4}x+\left(\frac{5}{8}\right)^{2}=\frac{1305}{4}+\left(\frac{5}{8}\right)^{2}$$

Pūruatia \frac{5}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{5}{4}x+\frac{25}{64}=\frac{1305}{4}+\frac{25}{64}$$

Tāpiri \frac{1305}{4} ki te \frac{25}{64} 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.

$$x^{2}+\frac{5}{4}x+\frac{25}{64}=\frac{20905}{64}$$

Tauwehea x^{2}+\frac{5}{4}x+\frac{25}{64}. 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}.

$$\left(x+\frac{5}{8}\right)^{2}=\frac{20905}{64}$$

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

$$\sqrt{\left(x+\frac{5}{8}\right)^{2}}=\sqrt{\frac{20905}{64}}$$

Whakarūnātia.

$$x+\frac{5}{8}=\frac{\sqrt{20905}}{8} x+\frac{5}{8}=-\frac{\sqrt{20905}}{8}$$

Me tango \frac{5}{8} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{20905}-5}{8} x=\frac{-\sqrt{20905}-5}{8}$$