Whakaoti i te (2x-1)(1+2x)+3(x+2)(x-2)=7(x-1)^2

$$( 2 x - 1 ) ( 1 + 2 x ) + 3 ( x + 2 ) ( x - 2 ) = 7 ( x - 1 ) ^ { 2 }$$

Whakaoti mō x

$$x = \frac{10}{7} = 1\frac{3}{7} \approx 1.428571429$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

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

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

$$4x^{2}-1+\left(3x+6\right)\left(x-2\right)=7\left(x-1\right)^{2}$$

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

$$4x^{2}-1+3x^{2}-12=7\left(x-1\right)^{2}$$

Pahekotia te 4x^{2} me 3x^{2}, ka 7x^{2}.

$$7x^{2}-1-12=7\left(x-1\right)^{2}$$

Tangohia te 12 i te -1, ka -13.

$$7x^{2}-13=7\left(x-1\right)^{2}$$

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

$$7x^{2}-13=7\left(x^{2}-2x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 7 ki te x^{2}-2x+1.

$$7x^{2}-13=7x^{2}-14x+7$$

Tangohia te 7x^{2} mai i ngā taha e rua.

$$7x^{2}-13-7x^{2}=-14x+7$$

Pahekotia te 7x^{2} me -7x^{2}, ka 0.

$$-13=-14x+7$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-14x+7=-13$$

Tangohia te 7 mai i ngā taha e rua.

$$-14x=-13-7$$

Tangohia te 7 i te -13, ka -20.

$$-14x=-20$$

Whakawehea ngā taha e rua ki te -14.

$$x=\frac{-20}{-14}$$

Whakahekea te hautanga \frac{-20}{-14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te -2.

$$x=\frac{10}{7}$$