Whakaoti i te 4(n^2-9)=3(n-12)

$$4 ( n ^ { 2 } - 9 ) = 3 ( n - 12 )$$

Whakaoti mō n

$$n=\frac{3}{4}=0.75$$

$$n=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te n^{2}-9.

$$4n^{2}-36=3\left(n-12\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te n-12.

$$4n^{2}-36=3n-36$$

Tangohia te 3n mai i ngā taha e rua.

$$4n^{2}-36-3n=-36$$

Me tāpiri te 36 ki ngā taha e rua.

$$4n^{2}-36-3n+36=0$$

Tāpirihia te -36 ki te 36, ka 0.

$$4n^{2}-3n=0$$

Tauwehea te n.

$$n\left(4n-3\right)=0$$

Hei kimi otinga whārite, me whakaoti te n=0 me te 4n-3=0.

$$n=0 n=\frac{3}{4}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te n^{2}-9.

$$4n^{2}-36=3\left(n-12\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te n-12.

$$4n^{2}-36=3n-36$$

Tangohia te 3n mai i ngā taha e rua.

$$4n^{2}-36-3n=-36$$

Me tāpiri te 36 ki ngā taha e rua.

$$4n^{2}-36-3n+36=0$$

Tāpirihia te -36 ki te 36, ka 0.

$$4n^{2}-3n=0$$

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

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

Tuhia te pūtakerua o te \left(-3\right)^{2}.

$$n=\frac{-\left(-3\right)±3}{2\times 4}$$

Ko te tauaro o -3 ko 3.

$$n=\frac{3±3}{2\times 4}$$

Whakareatia 2 ki te 4.

$$n=\frac{3±3}{8}$$

Nā, me whakaoti te whārite n=\frac{3±3}{8} ina he tāpiri te ±. Tāpiri 3 ki te 3.

$$n=\frac{6}{8}$$

Whakahekea te hautanga \frac{6}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$n=\frac{3}{4}$$

Nā, me whakaoti te whārite n=\frac{3±3}{8} ina he tango te ±. Tango 3 mai i 3.

$$n=\frac{0}{8}$$

Whakawehe 0 ki te 8.

$$n=0$$

Kua oti te whārite te whakatau.

$$n=\frac{3}{4} n=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te n^{2}-9.

$$4n^{2}-36=3\left(n-12\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te n-12.

$$4n^{2}-36=3n-36$$

Tangohia te 3n mai i ngā taha e rua.

$$4n^{2}-36-3n=-36$$

Me tāpiri te 36 ki ngā taha e rua.

$$4n^{2}-3n=-36+36$$

Tāpirihia te -36 ki te 36, ka 0.

$$4n^{2}-3n=0$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4n^{2}-3n}{4}=\frac{0}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$n^{2}-\frac{3}{4}n=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$n^{2}-\frac{3}{4}n=0$$

Whakawehea te -\frac{3}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{8}. Nā, tāpiria te pūrua o te -\frac{3}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$n^{2}-\frac{3}{4}n+\left(-\frac{3}{8}\right)^{2}=\left(-\frac{3}{8}\right)^{2}$$

Pūruatia -\frac{3}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$n^{2}-\frac{3}{4}n+\frac{9}{64}=\frac{9}{64}$$

Tauwehea n^{2}-\frac{3}{4}n+\frac{9}{64}. 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}.

$$\left(n-\frac{3}{8}\right)^{2}=\frac{9}{64}$$

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

$$\sqrt{\left(n-\frac{3}{8}\right)^{2}}=\sqrt{\frac{9}{64}}$$

Whakarūnātia.

$$n-\frac{3}{8}=\frac{3}{8} n-\frac{3}{8}=-\frac{3}{8}$$

Me tāpiri \frac{3}{8} ki ngā taha e rua o te whārite.

$$n=\frac{3}{4} n=0$$