Whakaoti i te x^2-13x+33=0

$$x ^ { 2 } - 13 x + 33 = 0$$

Whakaoti mō x

$$x = \frac{\sqrt{37} + 13}{2} \approx 9.541381265$$

$$x = \frac{13 - \sqrt{37}}{2} \approx 3.458618735$$

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.

$$x^{2}-13x+33=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -13 mō b, me 33 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 33}}{2}$$

Pūrua -13.

$$x=\frac{-\left(-13\right)±\sqrt{169-4\times 33}}{2}$$

Whakareatia -4 ki te 33.

$$x=\frac{-\left(-13\right)±\sqrt{169-132}}{2}$$

Tāpiri 169 ki te -132.

$$x=\frac{-\left(-13\right)±\sqrt{37}}{2}$$

Ko te tauaro o -13 ko 13.

$$x=\frac{13±\sqrt{37}}{2}$$

Nā, me whakaoti te whārite x=\frac{13±\sqrt{37}}{2} ina he tāpiri te ±. Tāpiri 13 ki te \sqrt{37}.

$$x=\frac{\sqrt{37}+13}{2}$$

Nā, me whakaoti te whārite x=\frac{13±\sqrt{37}}{2} ina he tango te ±. Tango \sqrt{37} mai i 13.

$$x=\frac{13-\sqrt{37}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{37}+13}{2} x=\frac{13-\sqrt{37}}{2}$$

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.

$$x^{2}-13x+33=0$$

Me tango 33 mai i ngā taha e rua o te whārite.

$$x^{2}-13x+33-33=-33$$

Mā te tango i te 33 i a ia ake anō ka toe ko te 0.

$$x^{2}-13x=-33$$

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.

$$x^{2}-13x+\left(-\frac{13}{2}\right)^{2}=-33+\left(-\frac{13}{2}\right)^{2}$$

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

$$x^{2}-13x+\frac{169}{4}=-33+\frac{169}{4}$$

Tāpiri -33 ki te \frac{169}{4}.

$$x^{2}-13x+\frac{169}{4}=\frac{37}{4}$$

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}.

$$\left(x-\frac{13}{2}\right)^{2}=\frac{37}{4}$$

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

$$\sqrt{\left(x-\frac{13}{2}\right)^{2}}=\sqrt{\frac{37}{4}}$$

Whakarūnātia.

$$x-\frac{13}{2}=\frac{\sqrt{37}}{2} x-\frac{13}{2}=-\frac{\sqrt{37}}{2}$$

Me tāpiri \frac{13}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{37}+13}{2} x=\frac{13-\sqrt{37}}{2}$$