Whakaoti i te x^2-20x+13=0

$$x ^ { 2 } - 20 x + 13 = 0$$

Whakaoti mō x

$$x=\sqrt{87}+10\approx 19.327379053$$

$$x=10-\sqrt{87}\approx 0.672620947$$

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.

$$x^{2}-20x+13=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -20 mō b, me 13 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 13}}{2}$$

Pūrua -20.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\times 13}}{2}$$

Whakareatia -4 ki te 13.

$$x=\frac{-\left(-20\right)±\sqrt{400-52}}{2}$$

Tāpiri 400 ki te -52.

$$x=\frac{-\left(-20\right)±\sqrt{348}}{2}$$

Tuhia te pūtakerua o te 348.

$$x=\frac{-\left(-20\right)±2\sqrt{87}}{2}$$

Ko te tauaro o -20 ko 20.

$$x=\frac{20±2\sqrt{87}}{2}$$

Nā, me whakaoti te whārite x=\frac{20±2\sqrt{87}}{2} ina he tāpiri te ±. Tāpiri 20 ki te 2\sqrt{87}.

$$x=\frac{2\sqrt{87}+20}{2}$$

Whakawehe 20+2\sqrt{87} ki te 2.

$$x=\sqrt{87}+10$$

Nā, me whakaoti te whārite x=\frac{20±2\sqrt{87}}{2} ina he tango te ±. Tango 2\sqrt{87} mai i 20.

$$x=\frac{20-2\sqrt{87}}{2}$$

Whakawehe 20-2\sqrt{87} ki te 2.

$$x=10-\sqrt{87}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{87}+10 x=10-\sqrt{87}$$

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.

$$x^{2}-20x+13=0$$

Me tango 13 mai i ngā taha e rua o te whārite.

$$x^{2}-20x+13-13=-13$$

Mā te tango i te 13 i a ia ake anō ka toe ko te 0.

$$x^{2}-20x=-13$$

Whakawehea te -20, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -10. Nā, tāpiria te pūrua o te -10 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-20x+\left(-10\right)^{2}=-13+\left(-10\right)^{2}$$

Pūrua -10.

$$x^{2}-20x+100=-13+100$$

Tāpiri -13 ki te 100.

$$x^{2}-20x+100=87$$

Tauwehea x^{2}-20x+100. 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}.

$$\left(x-10\right)^{2}=87$$

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

$$\sqrt{\left(x-10\right)^{2}}=\sqrt{87}$$

Whakarūnātia.

$$x-10=\sqrt{87} x-10=-\sqrt{87}$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$x=\sqrt{87}+10 x=10-\sqrt{87}$$