Whakaoti i te 12x-3=x^2

$$12 x - 3 = x ^ { 2 }$$

Whakaoti mō x

$$x=\sqrt{33}+6\approx 11.744562647$$

$$x=6-\sqrt{33}\approx 0.255437353$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

$$12x-3-x^{2}=0$$

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.

$$-x^{2}+12x-3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 12 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-1\right)\left(-3\right)}}{2\left(-1\right)}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\left(-1\right)\left(-3\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-12±\sqrt{144+4\left(-3\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -3.

$$x=\frac{-12±\sqrt{144-12}}{2\left(-1\right)}$$

Tāpiri 144 ki te -12.

$$x=\frac{-12±\sqrt{132}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 132.

$$x=\frac{-12±2\sqrt{33}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-12±2\sqrt{33}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-12±2\sqrt{33}}{-2} ina he tāpiri te ±. Tāpiri -12 ki te 2\sqrt{33}.

$$x=\frac{2\sqrt{33}-12}{-2}$$

Whakawehe -12+2\sqrt{33} ki te -2.

$$x=6-\sqrt{33}$$

Nā, me whakaoti te whārite x=\frac{-12±2\sqrt{33}}{-2} ina he tango te ±. Tango 2\sqrt{33} mai i -12.

$$x=\frac{-2\sqrt{33}-12}{-2}$$

Whakawehe -12-2\sqrt{33} ki te -2.

$$x=\sqrt{33}+6$$

Kua oti te whārite te whakatau.

$$x=6-\sqrt{33} x=\sqrt{33}+6$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

$$12x-3-x^{2}=0$$

Me tāpiri te 3 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$12x-x^{2}=3$$

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.

$$-x^{2}+12x=3$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+12x}{-1}=\frac{3}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{12}{-1}x=\frac{3}{-1}$$

Whakawehe 12 ki te -1.

$$x^{2}-12x=\frac{3}{-1}$$

Whakawehe 3 ki te -1.

$$x^{2}-12x=-3$$

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.

$$x^{2}-12x+\left(-6\right)^{2}=-3+\left(-6\right)^{2}$$

Pūrua -6.

$$x^{2}-12x+36=-3+36$$

Tāpiri -3 ki te 36.

$$x^{2}-12x+36=33$$

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}.

$$\left(x-6\right)^{2}=33$$

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

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{33}$$

Whakarūnātia.

$$x-6=\sqrt{33} x-6=-\sqrt{33}$$

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

$$x=\sqrt{33}+6 x=6-\sqrt{33}$$