Whakaoti i te y^2+5y=625

$$y ^ { 2 } + 5 y = 625$$

Whakaoti mō y

$$y = \frac{5 \sqrt{101} - 5}{2} \approx 22.624689053$$

$$y=\frac{-5\sqrt{101}-5}{2}\approx -27.624689053$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$y^{2}+5y=625$$

Me tango 625 mai i ngā taha e rua o te whārite.

$$y^{2}+5y-625=625-625$$

Mā te tango i te 625 i a ia ake anō ka toe ko te 0.

$$y^{2}+5y-625=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 5 mō b, me -625 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-5±\sqrt{5^{2}-4\left(-625\right)}}{2}$$

Pūrua 5.

$$y=\frac{-5±\sqrt{25-4\left(-625\right)}}{2}$$

Whakareatia -4 ki te -625.

$$y=\frac{-5±\sqrt{25+2500}}{2}$$

Tāpiri 25 ki te 2500.

$$y=\frac{-5±\sqrt{2525}}{2}$$

Tuhia te pūtakerua o te 2525.

$$y=\frac{-5±5\sqrt{101}}{2}$$

Nā, me whakaoti te whārite y=\frac{-5±5\sqrt{101}}{2} ina he tāpiri te ±. Tāpiri -5 ki te 5\sqrt{101}.

$$y=\frac{5\sqrt{101}-5}{2}$$

Nā, me whakaoti te whārite y=\frac{-5±5\sqrt{101}}{2} ina he tango te ±. Tango 5\sqrt{101} mai i -5.

$$y=\frac{-5\sqrt{101}-5}{2}$$

Kua oti te whārite te whakatau.

$$y=\frac{5\sqrt{101}-5}{2} y=\frac{-5\sqrt{101}-5}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$y^{2}+5y=625$$

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

$$y^{2}+5y+\left(\frac{5}{2}\right)^{2}=625+\left(\frac{5}{2}\right)^{2}$$

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

$$y^{2}+5y+\frac{25}{4}=625+\frac{25}{4}$$

Tāpiri 625 ki te \frac{25}{4}.

$$y^{2}+5y+\frac{25}{4}=\frac{2525}{4}$$

Tauwehea y^{2}+5y+\frac{25}{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}.

$$\left(y+\frac{5}{2}\right)^{2}=\frac{2525}{4}$$

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

$$\sqrt{\left(y+\frac{5}{2}\right)^{2}}=\sqrt{\frac{2525}{4}}$$

Whakarūnātia.

$$y+\frac{5}{2}=\frac{5\sqrt{101}}{2} y+\frac{5}{2}=-\frac{5\sqrt{101}}{2}$$

Me tango \frac{5}{2} mai i ngā taha e rua o te whārite.

$$y=\frac{5\sqrt{101}-5}{2} y=\frac{-5\sqrt{101}-5}{2}$$