Whakaoti i te 3x^2-36x+95=0

$$3 x ^ { 2 } - 36 x + 95 = 0$$

Whakaoti mō x

$$x=\frac{\sqrt{39}}{3}+6\approx 8.081665999$$

$$x=-\frac{\sqrt{39}}{3}+6\approx 3.918334001$$

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.

$$3x^{2}-36x+95=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -36 mō b, me 95 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 3\times 95}}{2\times 3}$$

Pūrua -36.

$$x=\frac{-\left(-36\right)±\sqrt{1296-4\times 3\times 95}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-36\right)±\sqrt{1296-12\times 95}}{2\times 3}$$

Whakareatia -12 ki te 95.

$$x=\frac{-\left(-36\right)±\sqrt{1296-1140}}{2\times 3}$$

Tāpiri 1296 ki te -1140.

$$x=\frac{-\left(-36\right)±\sqrt{156}}{2\times 3}$$

Tuhia te pūtakerua o te 156.

$$x=\frac{-\left(-36\right)±2\sqrt{39}}{2\times 3}$$

Ko te tauaro o -36 ko 36.

$$x=\frac{36±2\sqrt{39}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{36±2\sqrt{39}}{6}$$

Nā, me whakaoti te whārite x=\frac{36±2\sqrt{39}}{6} ina he tāpiri te ±. Tāpiri 36 ki te 2\sqrt{39}.

$$x=\frac{2\sqrt{39}+36}{6}$$

Whakawehe 36+2\sqrt{39} ki te 6.

$$x=\frac{\sqrt{39}}{3}+6$$

Nā, me whakaoti te whārite x=\frac{36±2\sqrt{39}}{6} ina he tango te ±. Tango 2\sqrt{39} mai i 36.

$$x=\frac{36-2\sqrt{39}}{6}$$

Whakawehe 36-2\sqrt{39} ki te 6.

$$x=-\frac{\sqrt{39}}{3}+6$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{39}}{3}+6 x=-\frac{\sqrt{39}}{3}+6$$

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.

$$3x^{2}-36x+95=0$$

Me tango 95 mai i ngā taha e rua o te whārite.

$$3x^{2}-36x+95-95=-95$$

Mā te tango i te 95 i a ia ake anō ka toe ko te 0.

$$3x^{2}-36x=-95$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}-36x}{3}=-\frac{95}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$x^{2}+\left(-\frac{36}{3}\right)x=-\frac{95}{3}$$

Whakawehe -36 ki te 3.

$$x^{2}-12x=-\frac{95}{3}$$

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.

$$x^{2}-12x+\left(-6\right)^{2}=-\frac{95}{3}+\left(-6\right)^{2}$$

Pūrua -6.

$$x^{2}-12x+36=-\frac{95}{3}+36$$

Tāpiri -\frac{95}{3} ki te 36.

$$x^{2}-12x+36=\frac{13}{3}$$

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}.

$$\left(x-6\right)^{2}=\frac{13}{3}$$

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

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{\frac{13}{3}}$$

Whakarūnātia.

$$x-6=\frac{\sqrt{39}}{3} x-6=-\frac{\sqrt{39}}{3}$$

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

$$x=\frac{\sqrt{39}}{3}+6 x=-\frac{\sqrt{39}}{3}+6$$