Whakaoti i te (x-4)(4x-3)=12

$$( x - 4 ) ( 4 x - 3 ) = 12$$

Whakaoti mō x

$$x = \frac{19}{4} = 4\frac{3}{4} = 4.75$$

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-4 ki te 4x-3 ka whakakotahi i ngā kupu rite.

$$4x^{2}-19x+12=12$$

Tangohia te 12 mai i ngā taha e rua.

$$4x^{2}-19x+12-12=0$$

Tangohia te 12 i te 12, ka 0.

$$4x^{2}-19x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, -19 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-19\right)±\sqrt{\left(-19\right)^{2}}}{2\times 4}$$

Tuhia te pūtakerua o te \left(-19\right)^{2}.

$$x=\frac{-\left(-19\right)±19}{2\times 4}$$

Ko te tauaro o -19 ko 19.

$$x=\frac{19±19}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{19±19}{8}$$

Nā, me whakaoti te whārite x=\frac{19±19}{8} ina he tāpiri te ±. Tāpiri 19 ki te 19.

$$x=\frac{38}{8}$$

Whakahekea te hautanga \frac{38}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{19}{4}$$

Nā, me whakaoti te whārite x=\frac{19±19}{8} ina he tango te ±. Tango 19 mai i 19.

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

Whakawehe 0 ki te 8.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{19}{4} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-4 ki te 4x-3 ka whakakotahi i ngā kupu rite.

$$4x^{2}-19x+12=12$$

Tangohia te 12 mai i ngā taha e rua.

$$4x^{2}-19x=12-12$$

Tangohia te 12 i te 12, ka 0.

$$4x^{2}-19x=0$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}-19x}{4}=\frac{0}{4}$$

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

$$x^{2}-\frac{19}{4}x=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$x^{2}-\frac{19}{4}x=0$$

Whakawehea te -\frac{19}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{19}{8}. Nā, tāpiria te pūrua o te -\frac{19}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{19}{4}x+\left(-\frac{19}{8}\right)^{2}=\left(-\frac{19}{8}\right)^{2}$$

Pūruatia -\frac{19}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{19}{4}x+\frac{361}{64}=\frac{361}{64}$$

Tauwehea x^{2}-\frac{19}{4}x+\frac{361}{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}.

$$\left(x-\frac{19}{8}\right)^{2}=\frac{361}{64}$$

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

$$\sqrt{\left(x-\frac{19}{8}\right)^{2}}=\sqrt{\frac{361}{64}}$$

Whakarūnātia.

$$x-\frac{19}{8}=\frac{19}{8} x-\frac{19}{8}=-\frac{19}{8}$$

Me tāpiri \frac{19}{8} ki ngā taha e rua o te whārite.

$$x=\frac{19}{4} x=0$$