Whakaoti i te 4x(x-3)=16x

$$4 x ( x - 3 ) = 16 x$$

Whakaoti mō x

$$x=7$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x-3.

$$4x^{2}-12x=16x$$

Tangohia te 16x mai i ngā taha e rua.

$$4x^{2}-12x-16x=0$$

Pahekotia te -12x me -16x, ka -28x.

$$4x^{2}-28x=0$$

Tauwehea te x.

$$x\left(4x-28\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 4x-28=0.

$$x=0 x=7$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x-3.

$$4x^{2}-12x=16x$$

Tangohia te 16x mai i ngā taha e rua.

$$4x^{2}-12x-16x=0$$

Pahekotia te -12x me -16x, ka -28x.

$$4x^{2}-28x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, -28 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-28\right)±\sqrt{\left(-28\right)^{2}}}{2\times 4}$$

Tuhia te pūtakerua o te \left(-28\right)^{2}.

$$x=\frac{-\left(-28\right)±28}{2\times 4}$$

Ko te tauaro o -28 ko 28.

$$x=\frac{28±28}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{28±28}{8}$$

Nā, me whakaoti te whārite x=\frac{28±28}{8} ina he tāpiri te ±. Tāpiri 28 ki te 28.

$$x=\frac{56}{8}$$

Whakawehe 56 ki te 8.

$$x=7$$

Nā, me whakaoti te whārite x=\frac{28±28}{8} ina he tango te ±. Tango 28 mai i 28.

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

Whakawehe 0 ki te 8.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=7 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x-3.

$$4x^{2}-12x=16x$$

Tangohia te 16x mai i ngā taha e rua.

$$4x^{2}-12x-16x=0$$

Pahekotia te -12x me -16x, ka -28x.

$$4x^{2}-28x=0$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}-28x}{4}=\frac{0}{4}$$

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

$$x^{2}+\left(-\frac{28}{4}\right)x=\frac{0}{4}$$

Whakawehe -28 ki te 4.

$$x^{2}-7x=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$x^{2}-7x=0$$

Whakawehea te -7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{2}. Nā, tāpiria te pūrua o te -\frac{7}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Pūruatia -\frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-7x+\frac{49}{4}=\frac{49}{4}$$

Tauwehea x^{2}-7x+\frac{49}{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}.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

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

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Whakarūnātia.

$$x-\frac{7}{2}=\frac{7}{2} x-\frac{7}{2}=-\frac{7}{2}$$

Me tāpiri \frac{7}{2} ki ngā taha e rua o te whārite.

$$x=7 x=0$$