Whakaoti i te 24x^2-72x+48=0

$$24 x ^ { 2 } - 72 x + 48 = 0$$

Whakaoti mō x

$$x=1$$

$$x=2$$

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.

$$24x^{2}-72x+48=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 24 mō a, -72 mō b, me 48 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}-4\times 24\times 48}}{2\times 24}$$

Pūrua -72.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4\times 24\times 48}}{2\times 24}$$

Whakareatia -4 ki te 24.

$$x=\frac{-\left(-72\right)±\sqrt{5184-96\times 48}}{2\times 24}$$

Whakareatia -96 ki te 48.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4608}}{2\times 24}$$

Tāpiri 5184 ki te -4608.

$$x=\frac{-\left(-72\right)±\sqrt{576}}{2\times 24}$$

Tuhia te pūtakerua o te 576.

$$x=\frac{-\left(-72\right)±24}{2\times 24}$$

Ko te tauaro o -72 ko 72.

$$x=\frac{72±24}{2\times 24}$$

Whakareatia 2 ki te 24.

$$x=\frac{72±24}{48}$$

Nā, me whakaoti te whārite x=\frac{72±24}{48} ina he tāpiri te ±. Tāpiri 72 ki te 24.

$$x=\frac{96}{48}$$

Whakawehe 96 ki te 48.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{72±24}{48} ina he tango te ±. Tango 24 mai i 72.

$$x=\frac{48}{48}$$

Whakawehe 48 ki te 48.

$$x=1$$

Kua oti te whārite te whakatau.

$$x=2 x=1$$

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.

$$24x^{2}-72x+48=0$$

Me tango 48 mai i ngā taha e rua o te whārite.

$$24x^{2}-72x+48-48=-48$$

Mā te tango i te 48 i a ia ake anō ka toe ko te 0.

$$24x^{2}-72x=-48$$

Whakawehea ngā taha e rua ki te 24.

$$\frac{24x^{2}-72x}{24}=-\frac{48}{24}$$

Mā te whakawehe ki te 24 ka wetekia te whakareanga ki te 24.

$$x^{2}+\left(-\frac{72}{24}\right)x=-\frac{48}{24}$$

Whakawehe -72 ki te 24.

$$x^{2}-3x=-\frac{48}{24}$$

Whakawehe -48 ki te 24.

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

Whakawehea te -3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{2}. Nā, tāpiria te pūrua o te -\frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3x+\frac{9}{4}=-2+\frac{9}{4}$$

Tāpiri -2 ki te \frac{9}{4}.

$$x^{2}-3x+\frac{9}{4}=\frac{1}{4}$$

Tauwehea x^{2}-3x+\frac{9}{4}. 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}.

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

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

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

Whakarūnātia.

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

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$x=2 x=1$$