Whakaoti i te (1/2-x)^2+3x=1/4+x(x+2)

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

Whakaoti mō x (complex solution)

$$x\in \mathrm{C}$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\frac{1}{2}-x\right)^{2}.

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

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

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

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

$$\frac{1}{4}+2x+x^{2}=\frac{1}{4}+x^{2}+2x$$

Tangohia te \frac{1}{4} mai i ngā taha e rua.

$$\frac{1}{4}+2x+x^{2}-\frac{1}{4}=x^{2}+2x$$

Tangohia te \frac{1}{4} i te \frac{1}{4}, ka 0.

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

Tangohia te x^{2} mai i ngā taha e rua.

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

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

$$2x=2x$$

Tangohia te 2x mai i ngā taha e rua.

$$2x-2x=0$$

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

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$

He pono tēnei mō tētahi x ahakoa.

$$x\in \mathrm{C}$$

Whakaoti mō x

$$x\in \mathrm{R}$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(\frac{1}{2}-x\right)^{2}.

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

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

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

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

$$\frac{1}{4}+2x+x^{2}=\frac{1}{4}+x^{2}+2x$$

Tangohia te \frac{1}{4} mai i ngā taha e rua.

$$\frac{1}{4}+2x+x^{2}-\frac{1}{4}=x^{2}+2x$$

Tangohia te \frac{1}{4} i te \frac{1}{4}, ka 0.

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

Tangohia te x^{2} mai i ngā taha e rua.

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

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

$$2x=2x$$

Tangohia te 2x mai i ngā taha e rua.

$$2x-2x=0$$

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

$$0=0$$

Whakatauritea te 0 me te 0.

$$\text{true}$$

He pono tēnei mō tētahi x ahakoa.

$$x\in \mathrm{R}$$