Whakaoti i te x^2-50x-5.000=0

$$x ^ { 2 } - 50 x - 5.000 = 0$$

Whakaoti mō x

$$x=3\sqrt{70}+25\approx 50.099800796$$

$$x=25-3\sqrt{70}\approx -0.099800796$$

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.

$$x^{2}-50x-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -50 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}-4\left(-5\right)}}{2}$$

Pūrua -50.

$$x=\frac{-\left(-50\right)±\sqrt{2500-4\left(-5\right)}}{2}$$

Whakareatia -4 ki te -5.

$$x=\frac{-\left(-50\right)±\sqrt{2500+20}}{2}$$

Tāpiri 2500 ki te 20.

$$x=\frac{-\left(-50\right)±\sqrt{2520}}{2}$$

Tuhia te pūtakerua o te 2520.

$$x=\frac{-\left(-50\right)±6\sqrt{70}}{2}$$

Ko te tauaro o -50 ko 50.

$$x=\frac{50±6\sqrt{70}}{2}$$

Nā, me whakaoti te whārite x=\frac{50±6\sqrt{70}}{2} ina he tāpiri te ±. Tāpiri 50 ki te 6\sqrt{70}.

$$x=\frac{6\sqrt{70}+50}{2}$$

Whakawehe 50+6\sqrt{70} ki te 2.

$$x=3\sqrt{70}+25$$

Nā, me whakaoti te whārite x=\frac{50±6\sqrt{70}}{2} ina he tango te ±. Tango 6\sqrt{70} mai i 50.

$$x=\frac{50-6\sqrt{70}}{2}$$

Whakawehe 50-6\sqrt{70} ki te 2.

$$x=25-3\sqrt{70}$$

Kua oti te whārite te whakatau.

$$x=3\sqrt{70}+25 x=25-3\sqrt{70}$$

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.

$$x^{2}-50x-5=0$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$x^{2}-50x-5-\left(-5\right)=-\left(-5\right)$$

Mā te tango i te -5 i a ia ake anō ka toe ko te 0.

$$x^{2}-50x=-\left(-5\right)$$

Tango -5 mai i 0.

$$x^{2}-50x=5$$

Whakawehea te -50, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -25. Nā, tāpiria te pūrua o te -25 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-50x+\left(-25\right)^{2}=5+\left(-25\right)^{2}$$

Pūrua -25.

$$x^{2}-50x+625=5+625$$

Tāpiri 5 ki te 625.

$$x^{2}-50x+625=630$$

Tauwehea x^{2}-50x+625. 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}.

$$\left(x-25\right)^{2}=630$$

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

$$\sqrt{\left(x-25\right)^{2}}=\sqrt{630}$$

Whakarūnātia.

$$x-25=3\sqrt{70} x-25=-3\sqrt{70}$$

Me tāpiri 25 ki ngā taha e rua o te whārite.

$$x=3\sqrt{70}+25 x=25-3\sqrt{70}$$