Whakaoti i te x^2-95x+2100=0

$${ x }^{ 2 } -95x+2100=0$$

Whakaoti mō x

$$x=35$$

$$x=60$$

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.

$$x^{2}-95x+2100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -95 mō b, me 2100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-95\right)±\sqrt{\left(-95\right)^{2}-4\times 2100}}{2}$$

Pūrua -95.

$$x=\frac{-\left(-95\right)±\sqrt{9025-4\times 2100}}{2}$$

Whakareatia -4 ki te 2100.

$$x=\frac{-\left(-95\right)±\sqrt{9025-8400}}{2}$$

Tāpiri 9025 ki te -8400.

$$x=\frac{-\left(-95\right)±\sqrt{625}}{2}$$

Tuhia te pūtakerua o te 625.

$$x=\frac{-\left(-95\right)±25}{2}$$

Ko te tauaro o -95 ko 95.

$$x=\frac{95±25}{2}$$

Nā, me whakaoti te whārite x=\frac{95±25}{2} ina he tāpiri te ±. Tāpiri 95 ki te 25.

$$x=\frac{120}{2}$$

Whakawehe 120 ki te 2.

$$x=60$$

Nā, me whakaoti te whārite x=\frac{95±25}{2} ina he tango te ±. Tango 25 mai i 95.

$$x=\frac{70}{2}$$

Whakawehe 70 ki te 2.

$$x=35$$

Kua oti te whārite te whakatau.

$$x=60 x=35$$

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.

$$x^{2}-95x+2100=0$$

Me tango 2100 mai i ngā taha e rua o te whārite.

$$x^{2}-95x+2100-2100=-2100$$

Mā te tango i te 2100 i a ia ake anō ka toe ko te 0.

$$x^{2}-95x=-2100$$

Whakawehea te -95, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{95}{2}. Nā, tāpiria te pūrua o te -\frac{95}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-95x+\left(-\frac{95}{2}\right)^{2}=-2100+\left(-\frac{95}{2}\right)^{2}$$

Pūruatia -\frac{95}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-95x+\frac{9025}{4}=-2100+\frac{9025}{4}$$

Tāpiri -2100 ki te \frac{9025}{4}.

$$x^{2}-95x+\frac{9025}{4}=\frac{625}{4}$$

Tauwehea te x^{2}-95x+\frac{9025}{4}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{95}{2}\right)^{2}=\frac{625}{4}$$

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

$$\sqrt{\left(x-\frac{95}{2}\right)^{2}}=\sqrt{\frac{625}{4}}$$

Whakarūnātia.

$$x-\frac{95}{2}=\frac{25}{2} x-\frac{95}{2}=-\frac{25}{2}$$

Me tāpiri \frac{95}{2} ki ngā taha e rua o te whārite.

$$x=60 x=35$$