Whakaoti i te (x+3)^2+(x+5)(x-2)+4=2(x+7)(x-3)

$$( x + 3 ) ^ { 2 } + ( x + 5 ) ( x - 2 ) + 4 = 2 ( x + 7 ) ( x - 3 )$$

Whakaoti mō x

$$x=-45$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+3\right)^{2}.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te x+5 ki te x-2 ka whakakotahi i ngā kupu rite.

$$x^{2}+6x+9+x^{2}+3x-10+4=2\left(x+7\right)\left(x-3\right)$$

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

$$2x^{2}+6x+9+3x-10+4=2\left(x+7\right)\left(x-3\right)$$

Pahekotia te 6x me 3x, ka 9x.

$$2x^{2}+9x+9-10+4=2\left(x+7\right)\left(x-3\right)$$

Tangohia te 10 i te 9, ka -1.

$$2x^{2}+9x-1+4=2\left(x+7\right)\left(x-3\right)$$

Tāpirihia te -1 ki te 4, ka 3.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x+7.

$$2x^{2}+9x+3=\left(2x+14\right)\left(x-3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x+14 ki te x-3 ka whakakotahi i ngā kupu rite.

$$2x^{2}+9x+3=2x^{2}+8x-42$$

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

$$2x^{2}+9x+3-2x^{2}=8x-42$$

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

$$9x+3=8x-42$$

Tangohia te 8x mai i ngā taha e rua.

$$9x+3-8x=-42$$

Pahekotia te 9x me -8x, ka x.

$$x+3=-42$$

Tangohia te 3 mai i ngā taha e rua.

$$x=-42-3$$

Tangohia te 3 i te -42, ka -45.

$$x=-45$$