Whakaoti i te x^2-379x-188=303

$$x ^ { 2 } - 379 x - 188 = 303$$

Whakaoti mō x

$$x = \frac{\sqrt{145605} + 379}{2} \approx 380.291116145$$

$$x=\frac{379-\sqrt{145605}}{2}\approx -1.291116145$$

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.

$$x^{2}-379x-188=303$$

Me tango 303 mai i ngā taha e rua o te whārite.

$$x^{2}-379x-188-303=303-303$$

Mā te tango i te 303 i a ia ake anō ka toe ko te 0.

$$x^{2}-379x-188-303=0$$

Tango 303 mai i -188.

$$x^{2}-379x-491=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -379 mō b, me -491 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-379\right)±\sqrt{\left(-379\right)^{2}-4\left(-491\right)}}{2}$$

Pūrua -379.

$$x=\frac{-\left(-379\right)±\sqrt{143641-4\left(-491\right)}}{2}$$

Whakareatia -4 ki te -491.

$$x=\frac{-\left(-379\right)±\sqrt{143641+1964}}{2}$$

Tāpiri 143641 ki te 1964.

$$x=\frac{-\left(-379\right)±\sqrt{145605}}{2}$$

Ko te tauaro o -379 ko 379.

$$x=\frac{379±\sqrt{145605}}{2}$$

Nā, me whakaoti te whārite x=\frac{379±\sqrt{145605}}{2} ina he tāpiri te ±. Tāpiri 379 ki te \sqrt{145605}.

$$x=\frac{\sqrt{145605}+379}{2}$$

Nā, me whakaoti te whārite x=\frac{379±\sqrt{145605}}{2} ina he tango te ±. Tango \sqrt{145605} mai i 379.

$$x=\frac{379-\sqrt{145605}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{145605}+379}{2} x=\frac{379-\sqrt{145605}}{2}$$

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.

$$x^{2}-379x-188=303$$

Me tāpiri 188 ki ngā taha e rua o te whārite.

$$x^{2}-379x-188-\left(-188\right)=303-\left(-188\right)$$

Mā te tango i te -188 i a ia ake anō ka toe ko te 0.

$$x^{2}-379x=303-\left(-188\right)$$

Tango -188 mai i 303.

$$x^{2}-379x=491$$

Whakawehea te -379, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{379}{2}. Nā, tāpiria te pūrua o te -\frac{379}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-379x+\left(-\frac{379}{2}\right)^{2}=491+\left(-\frac{379}{2}\right)^{2}$$

Pūruatia -\frac{379}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-379x+\frac{143641}{4}=491+\frac{143641}{4}$$

Tāpiri 491 ki te \frac{143641}{4}.

$$x^{2}-379x+\frac{143641}{4}=\frac{145605}{4}$$

Tauwehea te x^{2}-379x+\frac{143641}{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}.

$$\left(x-\frac{379}{2}\right)^{2}=\frac{145605}{4}$$

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

$$\sqrt{\left(x-\frac{379}{2}\right)^{2}}=\sqrt{\frac{145605}{4}}$$

Whakarūnātia.

$$x-\frac{379}{2}=\frac{\sqrt{145605}}{2} x-\frac{379}{2}=-\frac{\sqrt{145605}}{2}$$

Me tāpiri \frac{379}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{145605}+379}{2} x=\frac{379-\sqrt{145605}}{2}$$