Whakaoti i te 2*(x-1)*(2+x)-3/2-(x+2)^2=x*(3-sqrt[5]{-1})-3-x/3

$$\frac { 2 \cdot ( x - 1 ) \cdot ( 2 + x ) - 3 } { 2 } - ( x + 2 ) ^ { 2 } = x \cdot ( 3 - \sqrt[ 5 ] { - 1 } ) - \frac { 3 - x } { 3 }$$

Whakaoti mō x

$$x=-\frac{39}{44}\approx -0.886363636$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3.

$$3\left(2\left(x-1\right)\left(2+x\right)-3\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x-1.

$$3\left(\left(2x-2\right)\left(2+x\right)-3\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

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

$$3\left(2x+2x^{2}-4-3\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Tangohia te 3 i te -4, ka -7.

$$3\left(2x+2x^{2}-7\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 2x+2x^{2}-7.

$$6x+6x^{2}-21-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

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

$$6x+6x^{2}-21-6\left(x^{2}+4x+4\right)=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -6 ki te x^{2}+4x+4.

$$6x+6x^{2}-21-6x^{2}-24x-24=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Pahekotia te 6x^{2} me -6x^{2}, ka 0.

$$6x-21-24x-24=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Pahekotia te 6x me -24x, ka -18x.

$$-18x-21-24=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Tangohia te 24 i te -21, ka -45.

$$-18x-45=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Tātaitia te \sqrt[5]{-1} kia tae ki -1.

$$-18x-45=6x\left(3-\left(-1\right)\right)-2\left(3-x\right)$$

Ko te tauaro o -1 ko 1.

$$-18x-45=6x\left(3+1\right)-2\left(3-x\right)$$

Tāpirihia te 3 ki te 1, ka 4.

$$-18x-45=6x\times 4-2\left(3-x\right)$$

Whakareatia te 6 ki te 4, ka 24.

$$-18x-45=24x-2\left(3-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te 3-x.

$$-18x-45=24x-6+2x$$

Pahekotia te 24x me 2x, ka 26x.

$$-18x-45=26x-6$$

Tangohia te 26x mai i ngā taha e rua.

$$-18x-45-26x=-6$$

Pahekotia te -18x me -26x, ka -44x.

$$-44x-45=-6$$

Me tāpiri te 45 ki ngā taha e rua.

$$-44x=-6+45$$

Tāpirihia te -6 ki te 45, ka 39.

$$-44x=39$$

Whakawehea ngā taha e rua ki te -44.

$$x=\frac{39}{-44}$$

Ka taea te hautanga \frac{39}{-44} te tuhi anō ko -\frac{39}{44} mā te tango i te tohu tōraro.

$$x=-\frac{39}{44}$$