Whakaoti i te 6794+x^2=165x

$$6794+ { x }^{ 2 } =165x$$

Whakaoti mō x

$$x=79$$

$$x=86$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 165x mai i ngā taha e rua.

$$6794+x^{2}-165x=0$$

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.

$$x^{2}-165x+6794=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -165 mō b, me 6794 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-165\right)±\sqrt{\left(-165\right)^{2}-4\times 6794}}{2}$$

Pūrua -165.

$$x=\frac{-\left(-165\right)±\sqrt{27225-4\times 6794}}{2}$$

Whakareatia -4 ki te 6794.

$$x=\frac{-\left(-165\right)±\sqrt{27225-27176}}{2}$$

Tāpiri 27225 ki te -27176.

$$x=\frac{-\left(-165\right)±\sqrt{49}}{2}$$

Tuhia te pūtakerua o te 49.

$$x=\frac{-\left(-165\right)±7}{2}$$

Ko te tauaro o -165 ko 165.

$$x=\frac{165±7}{2}$$

Nā, me whakaoti te whārite x=\frac{165±7}{2} ina he tāpiri te ±. Tāpiri 165 ki te 7.

$$x=\frac{172}{2}$$

Whakawehe 172 ki te 2.

$$x=86$$

Nā, me whakaoti te whārite x=\frac{165±7}{2} ina he tango te ±. Tango 7 mai i 165.

$$x=\frac{158}{2}$$

Whakawehe 158 ki te 2.

$$x=79$$

Kua oti te whārite te whakatau.

$$x=86 x=79$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 165x mai i ngā taha e rua.

$$6794+x^{2}-165x=0$$

Tangohia te 6794 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-165x=-6794$$

Whakawehea te -165, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{165}{2}. Nā, tāpiria te pūrua o te -\frac{165}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-165x+\left(-\frac{165}{2}\right)^{2}=-6794+\left(-\frac{165}{2}\right)^{2}$$

Pūruatia -\frac{165}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-165x+\frac{27225}{4}=-6794+\frac{27225}{4}$$

Tāpiri -6794 ki te \frac{27225}{4}.

$$x^{2}-165x+\frac{27225}{4}=\frac{49}{4}$$

Tauwehea x^{2}-165x+\frac{27225}{4}. 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}.

$$\left(x-\frac{165}{2}\right)^{2}=\frac{49}{4}$$

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

$$\sqrt{\left(x-\frac{165}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Whakarūnātia.

$$x-\frac{165}{2}=\frac{7}{2} x-\frac{165}{2}=-\frac{7}{2}$$

Me tāpiri \frac{165}{2} ki ngā taha e rua o te whārite.

$$x=86 x=79$$