Whakaoti i te 3x(x+1)-(x-2)^2-6=(x+3)(x-5)+x*(x+9)+5

$$3 x ( x + 1 ) - ( x - 2 ) ^ { 2 } - 6 = ( x + 3 ) ( x - 5 ) + x \cdot ( x + 9 ) + 5$$

Whakaoti mō x (complex solution)

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

Ngā Upane Otinga

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

$$3x^{2}+3x-\left(x-2\right)^{2}-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

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

$$3x^{2}+3x-\left(x^{2}-4x+4\right)-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Hei kimi i te tauaro o x^{2}-4x+4, kimihia te tauaro o ia taurangi.

$$3x^{2}+3x-x^{2}+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Pahekotia te 3x^{2} me -x^{2}, ka 2x^{2}.

$$2x^{2}+3x+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Pahekotia te 3x me 4x, ka 7x.

$$2x^{2}+7x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Tangohia te 6 i te -4, ka -10.

$$2x^{2}+7x-10=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+3 ki te x-5 ka whakakotahi i ngā kupu rite.

$$2x^{2}+7x-10=x^{2}-2x-15+x\left(x+9\right)+5$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+9.

$$2x^{2}+7x-10=x^{2}-2x-15+x^{2}+9x+5$$

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

$$2x^{2}+7x-10=2x^{2}-2x-15+9x+5$$

Pahekotia te -2x me 9x, ka 7x.

$$2x^{2}+7x-10=2x^{2}+7x-15+5$$

Tāpirihia te -15 ki te 5, ka -10.

$$2x^{2}+7x-10=2x^{2}+7x-10$$

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

$$2x^{2}+7x-10-2x^{2}=7x-10$$

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

$$7x-10=7x-10$$

Tangohia te 7x mai i ngā taha e rua.

$$7x-10-7x=-10$$

Pahekotia te 7x me -7x, ka 0.

$$-10=-10$$

Whakatauritea te -10 me te -10.

$$\text{true}$$

He pono tēnei mō tētahi x ahakoa.

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

Whakaoti mō x

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

Ngā Upane Otinga

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

$$3x^{2}+3x-\left(x-2\right)^{2}-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

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

$$3x^{2}+3x-\left(x^{2}-4x+4\right)-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Hei kimi i te tauaro o x^{2}-4x+4, kimihia te tauaro o ia taurangi.

$$3x^{2}+3x-x^{2}+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Pahekotia te 3x^{2} me -x^{2}, ka 2x^{2}.

$$2x^{2}+3x+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Pahekotia te 3x me 4x, ka 7x.

$$2x^{2}+7x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Tangohia te 6 i te -4, ka -10.

$$2x^{2}+7x-10=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+3 ki te x-5 ka whakakotahi i ngā kupu rite.

$$2x^{2}+7x-10=x^{2}-2x-15+x\left(x+9\right)+5$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+9.

$$2x^{2}+7x-10=x^{2}-2x-15+x^{2}+9x+5$$

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

$$2x^{2}+7x-10=2x^{2}-2x-15+9x+5$$

Pahekotia te -2x me 9x, ka 7x.

$$2x^{2}+7x-10=2x^{2}+7x-15+5$$

Tāpirihia te -15 ki te 5, ka -10.

$$2x^{2}+7x-10=2x^{2}+7x-10$$

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

$$2x^{2}+7x-10-2x^{2}=7x-10$$

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

$$7x-10=7x-10$$

Tangohia te 7x mai i ngā taha e rua.

$$7x-10-7x=-10$$

Pahekotia te 7x me -7x, ka 0.

$$-10=-10$$

Whakatauritea te -10 me te -10.

$$\text{true}$$

He pono tēnei mō tētahi x ahakoa.

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