Whakaoti i te x^2+3394*x+3976=0

$${ x }^{ 2 } +3394 \times x+3976=0$$

Whakaoti mō x

$$x=3\sqrt{319537}-1697\approx -1.17188371$$

$$x=-3\sqrt{319537}-1697\approx -3392.82811629$$

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.

$$x^{2}+3394x+3976=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 3394 mō b, me 3976 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3394±\sqrt{3394^{2}-4\times 3976}}{2}$$

Pūrua 3394.

$$x=\frac{-3394±\sqrt{11519236-4\times 3976}}{2}$$

Whakareatia -4 ki te 3976.

$$x=\frac{-3394±\sqrt{11519236-15904}}{2}$$

Tāpiri 11519236 ki te -15904.

$$x=\frac{-3394±\sqrt{11503332}}{2}$$

Tuhia te pūtakerua o te 11503332.

$$x=\frac{-3394±6\sqrt{319537}}{2}$$

Nā, me whakaoti te whārite x=\frac{-3394±6\sqrt{319537}}{2} ina he tāpiri te ±. Tāpiri -3394 ki te 6\sqrt{319537}.

$$x=\frac{6\sqrt{319537}-3394}{2}$$

Whakawehe -3394+6\sqrt{319537} ki te 2.

$$x=3\sqrt{319537}-1697$$

Nā, me whakaoti te whārite x=\frac{-3394±6\sqrt{319537}}{2} ina he tango te ±. Tango 6\sqrt{319537} mai i -3394.

$$x=\frac{-6\sqrt{319537}-3394}{2}$$

Whakawehe -3394-6\sqrt{319537} ki te 2.

$$x=-3\sqrt{319537}-1697$$

Kua oti te whārite te whakatau.

$$x=3\sqrt{319537}-1697 x=-3\sqrt{319537}-1697$$

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.

$$x^{2}+3394x+3976=0$$

Me tango 3976 mai i ngā taha e rua o te whārite.

$$x^{2}+3394x+3976-3976=-3976$$

Mā te tango i te 3976 i a ia ake anō ka toe ko te 0.

$$x^{2}+3394x=-3976$$

Whakawehea te 3394, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1697. Nā, tāpiria te pūrua o te 1697 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+3394x+1697^{2}=-3976+1697^{2}$$

Pūrua 1697.

$$x^{2}+3394x+2879809=-3976+2879809$$

Tāpiri -3976 ki te 2879809.

$$x^{2}+3394x+2879809=2875833$$

Tauwehea x^{2}+3394x+2879809. 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}.

$$\left(x+1697\right)^{2}=2875833$$

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

$$\sqrt{\left(x+1697\right)^{2}}=\sqrt{2875833}$$

Whakarūnātia.

$$x+1697=3\sqrt{319537} x+1697=-3\sqrt{319537}$$

Me tango 1697 mai i ngā taha e rua o te whārite.

$$x=3\sqrt{319537}-1697 x=-3\sqrt{319537}-1697$$