Whakaoti i te x^2+13x=2

$$x ^ { 2 } + 13 x = 2$$

Whakaoti mō x

$$x=\frac{\sqrt{177}-13}{2}\approx 0.152067348$$

$$x=\frac{-\sqrt{177}-13}{2}\approx -13.152067348$$

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.

$$x^{2}+13x=2$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$x^{2}+13x-2=2-2$$

Mā te tango i te 2 i a ia ake anō ka toe ko te 0.

$$x^{2}+13x-2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 13 mō b, me -2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-13±\sqrt{13^{2}-4\left(-2\right)}}{2}$$

Pūrua 13.

$$x=\frac{-13±\sqrt{169-4\left(-2\right)}}{2}$$

Whakareatia -4 ki te -2.

$$x=\frac{-13±\sqrt{169+8}}{2}$$

Tāpiri 169 ki te 8.

$$x=\frac{-13±\sqrt{177}}{2}$$

Nā, me whakaoti te whārite x=\frac{-13±\sqrt{177}}{2} ina he tāpiri te ±. Tāpiri -13 ki te \sqrt{177}.

$$x=\frac{\sqrt{177}-13}{2}$$

Nā, me whakaoti te whārite x=\frac{-13±\sqrt{177}}{2} ina he tango te ±. Tango \sqrt{177} mai i -13.

$$x=\frac{-\sqrt{177}-13}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{177}-13}{2} x=\frac{-\sqrt{177}-13}{2}$$

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.

$$x^{2}+13x=2$$

Whakawehea te 13, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{13}{2}. Nā, tāpiria te pūrua o te \frac{13}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+13x+\left(\frac{13}{2}\right)^{2}=2+\left(\frac{13}{2}\right)^{2}$$

Pūruatia \frac{13}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+13x+\frac{169}{4}=2+\frac{169}{4}$$

Tāpiri 2 ki te \frac{169}{4}.

$$x^{2}+13x+\frac{169}{4}=\frac{177}{4}$$

Tauwehea x^{2}+13x+\frac{169}{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}.

$$\left(x+\frac{13}{2}\right)^{2}=\frac{177}{4}$$

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

$$\sqrt{\left(x+\frac{13}{2}\right)^{2}}=\sqrt{\frac{177}{4}}$$

Whakarūnātia.

$$x+\frac{13}{2}=\frac{\sqrt{177}}{2} x+\frac{13}{2}=-\frac{\sqrt{177}}{2}$$

Me tango \frac{13}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{177}-13}{2} x=\frac{-\sqrt{177}-13}{2}$$