Whakaoti i te (a+10)^2=(a-d+10)(a+d+11)

$$( a + 10 ) ^ { 2 } = ( a - d + 10 ) ( a + d + 11 )$$

Whakaoti mō a

$$a=d^{2}+d-10$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(a+10\right)^{2}.

$$a^{2}+20a+100=\left(a-d+10\right)\left(a+d+11\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te a-d+10 ki te a+d+11 ka whakakotahi i ngā kupu rite.

$$a^{2}+20a+100=a^{2}+21a-d^{2}-d+110$$

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

$$a^{2}+20a+100-a^{2}=21a-d^{2}-d+110$$

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

$$20a+100=21a-d^{2}-d+110$$

Tangohia te 21a mai i ngā taha e rua.

$$20a+100-21a=-d^{2}-d+110$$

Pahekotia te 20a me -21a, ka -a.

$$-a+100=-d^{2}-d+110$$

Tangohia te 100 mai i ngā taha e rua.

$$-a=-d^{2}-d+110-100$$

Tangohia te 100 i te 110, ka 10.

$$-a=-d^{2}-d+10$$

He hanga arowhānui tō te whārite.

$$-a=10-d-d^{2}$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-a}{-1}=\frac{10-d-d^{2}}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$a=\frac{10-d-d^{2}}{-1}$$

Whakawehe -d^{2}-d+10 ki te -1.

$$a=d^{2}+d-10$$

Whakaoti mō d (complex solution)

$$d=\frac{\sqrt{4a+41}-1}{2}$$

$$d=\frac{-\sqrt{4a+41}-1}{2}$$

Whakaoti mō d

$$d=\frac{\sqrt{4a+41}-1}{2}$$

$$d=\frac{-\sqrt{4a+41}-1}{2}\text{, }a\geq -\frac{41}{4}$$