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

$$( 3 x + 1 ) ( 3 x - 1 ) + \frac { ( x - 2 ) ^ { 2 } } { 2 } = 1 - 2 x$$

Whakaoti mō x

$$x=0$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia ngā taha e rua o te whārite ki te 2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 3x+1.

$$\left(6x+2\right)\left(3x-1\right)+\left(x-2\right)^{2}=2-4x$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 6x+2 ki te 3x-1 ka whakakotahi i ngā kupu rite.

$$18x^{2}-2+\left(x-2\right)^{2}=2-4x$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-2\right)^{2}.

$$18x^{2}-2+x^{2}-4x+4=2-4x$$

Pahekotia te 18x^{2} me x^{2}, ka 19x^{2}.

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

Tāpirihia te -2 ki te 4, ka 2.

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

Me tāpiri te 4x ki ngā taha e rua.

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

Pahekotia te -4x me 4x, ka 0.

$$19x^{2}+2=2$$

Tangohia te 2 mai i ngā taha e rua.

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

Tangohia te 2 i te 2, ka 0.

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

Whakawehea ngā taha e rua ki te 19. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$x^{2}=0$$

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

$$x=0 x=0$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 3x+1.

$$\left(6x+2\right)\left(3x-1\right)+\left(x-2\right)^{2}=2-4x$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 6x+2 ki te 3x-1 ka whakakotahi i ngā kupu rite.

$$18x^{2}-2+\left(x-2\right)^{2}=2-4x$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-2\right)^{2}.

$$18x^{2}-2+x^{2}-4x+4=2-4x$$

Pahekotia te 18x^{2} me x^{2}, ka 19x^{2}.

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

Tāpirihia te -2 ki te 4, ka 2.

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

Tangohia te 2 mai i ngā taha e rua.

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

Tangohia te 2 i te 2, ka 0.

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

Me tāpiri te 4x ki ngā taha e rua.

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

Pahekotia te -4x me 4x, ka 0.

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

Whakawehea ngā taha e rua ki te 19. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$x^{2}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Tuhia te pūtakerua o te 0^{2}.

$$x=\frac{0±0}{2}$$

Whakawehe 0 ki te 2.

$$x=0$$