Whakaoti i te 3x(x+1)-x=2(x+54)

$$3x(x+1)-x=2(x+54)$$

Whakaoti mō x

$$x=-6$$

$$x=6$$

Ngā Upane mā te Kimi Pūtakerua

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x+1.

$$3x^{2}+3x-x=2\left(x+54\right)$$

Pahekotia te 3x me -x, ka 2x.

$$3x^{2}+2x=2\left(x+54\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x+54.

$$3x^{2}+2x=2x+108$$

Tangohia te 2x mai i ngā taha e rua.

$$3x^{2}+2x-2x=108$$

Pahekotia te 2x me -2x, ka 0.

$$3x^{2}=108$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=\frac{108}{3}$$

Whakawehea te 108 ki te 3, kia riro ko 36.

$$x^{2}=36$$

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

$$x=6 x=-6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x+1.

$$3x^{2}+3x-x=2\left(x+54\right)$$

Pahekotia te 3x me -x, ka 2x.

$$3x^{2}+2x=2\left(x+54\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x+54.

$$3x^{2}+2x=2x+108$$

Tangohia te 2x mai i ngā taha e rua.

$$3x^{2}+2x-2x=108$$

Pahekotia te 2x me -2x, ka 0.

$$3x^{2}=108$$

Tangohia te 108 mai i ngā taha e rua.

$$3x^{2}-108=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me -108 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-108\right)}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-108\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\left(-108\right)}}{2\times 3}$$

Whakareatia -12 ki te -108.

$$x=\frac{0±\sqrt{1296}}{2\times 3}$$

Tuhia te pūtakerua o te 1296.

$$x=\frac{0±36}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±36}{6}$$

Nā, me whakaoti te whārite x=\frac{0±36}{6} ina he tāpiri te ±. Whakawehe 36 ki te 6.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{0±36}{6} ina he tango te ±. Whakawehe -36 ki te 6.

$$x=-6$$

Kua oti te whārite te whakatau.

$$x=6 x=-6$$