Whakaoti i te x^2+8x-2400=0

$$x ^ { 2 } + 8 x - 2400 = 0$$

Whakaoti mō x

$$x=4\sqrt{151}-4\approx 45.15282291$$

$$x=-4\sqrt{151}-4\approx -53.15282291$$

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.

$$x^{2}+8x-2400=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 8 mō b, me -2400 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-2400\right)}}{2}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-2400\right)}}{2}$$

Whakareatia -4 ki te -2400.

$$x=\frac{-8±\sqrt{64+9600}}{2}$$

Tāpiri 64 ki te 9600.

$$x=\frac{-8±\sqrt{9664}}{2}$$

Tuhia te pūtakerua o te 9664.

$$x=\frac{-8±8\sqrt{151}}{2}$$

Nā, me whakaoti te whārite x=\frac{-8±8\sqrt{151}}{2} ina he tāpiri te ±. Tāpiri -8 ki te 8\sqrt{151}.

$$x=\frac{8\sqrt{151}-8}{2}$$

Whakawehe -8+8\sqrt{151} ki te 2.

$$x=4\sqrt{151}-4$$

Nā, me whakaoti te whārite x=\frac{-8±8\sqrt{151}}{2} ina he tango te ±. Tango 8\sqrt{151} mai i -8.

$$x=\frac{-8\sqrt{151}-8}{2}$$

Whakawehe -8-8\sqrt{151} ki te 2.

$$x=-4\sqrt{151}-4$$

Kua oti te whārite te whakatau.

$$x=4\sqrt{151}-4 x=-4\sqrt{151}-4$$

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.

$$x^{2}+8x-2400=0$$

Me tāpiri 2400 ki ngā taha e rua o te whārite.

$$x^{2}+8x-2400-\left(-2400\right)=-\left(-2400\right)$$

Mā te tango i te -2400 i a ia ake anō ka toe ko te 0.

$$x^{2}+8x=-\left(-2400\right)$$

Tango -2400 mai i 0.

$$x^{2}+8x=2400$$

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

$$x^{2}+8x+4^{2}=2400+4^{2}$$

Pūrua 4.

$$x^{2}+8x+16=2400+16$$

Tāpiri 2400 ki te 16.

$$x^{2}+8x+16=2416$$

Tauwehea x^{2}+8x+16. 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}.

$$\left(x+4\right)^{2}=2416$$

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

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{2416}$$

Whakarūnātia.

$$x+4=4\sqrt{151} x+4=-4\sqrt{151}$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$x=4\sqrt{151}-4 x=-4\sqrt{151}-4$$