Whakaoti i te x^2-12x=11

$$x ^ { 2 } - 12 x = 11$$

Whakaoti mō x

$$x=\sqrt{47}+6\approx 12.8556546$$

$$x=6-\sqrt{47}\approx -0.8556546$$

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.

$$x^{2}-12x=11$$

Me tango 11 mai i ngā taha e rua o te whārite.

$$x^{2}-12x-11=11-11$$

Mā te tango i te 11 i a ia ake anō ka toe ko te 0.

$$x^{2}-12x-11=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -12 mō b, me -11 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-11\right)}}{2}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-11\right)}}{2}$$

Whakareatia -4 ki te -11.

$$x=\frac{-\left(-12\right)±\sqrt{144+44}}{2}$$

Tāpiri 144 ki te 44.

$$x=\frac{-\left(-12\right)±\sqrt{188}}{2}$$

Tuhia te pūtakerua o te 188.

$$x=\frac{-\left(-12\right)±2\sqrt{47}}{2}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±2\sqrt{47}}{2}$$

Nā, me whakaoti te whārite x=\frac{12±2\sqrt{47}}{2} ina he tāpiri te ±. Tāpiri 12 ki te 2\sqrt{47}.

$$x=\frac{2\sqrt{47}+12}{2}$$

Whakawehe 12+2\sqrt{47} ki te 2.

$$x=\sqrt{47}+6$$

Nā, me whakaoti te whārite x=\frac{12±2\sqrt{47}}{2} ina he tango te ±. Tango 2\sqrt{47} mai i 12.

$$x=\frac{12-2\sqrt{47}}{2}$$

Whakawehe 12-2\sqrt{47} ki te 2.

$$x=6-\sqrt{47}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{47}+6 x=6-\sqrt{47}$$

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.

$$x^{2}-12x=11$$

Whakawehea te -12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -6. Nā, tāpiria te pūrua o te -6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-12x+\left(-6\right)^{2}=11+\left(-6\right)^{2}$$

Pūrua -6.

$$x^{2}-12x+36=11+36$$

Tāpiri 11 ki te 36.

$$x^{2}-12x+36=47$$

Tauwehea x^{2}-12x+36. 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}.

$$\left(x-6\right)^{2}=47$$

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

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{47}$$

Whakarūnātia.

$$x-6=\sqrt{47} x-6=-\sqrt{47}$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$x=\sqrt{47}+6 x=6-\sqrt{47}$$