Whakaoti i te (x-7)^2-x(6+x)operatorname{mon}x=-1/20

$$( x - 7 ) ^ { 2 } - x ( 6 + x ) \operatorname { mon } x = - \frac { 1 } { 20 }$$

Whakaoti mō m (complex solution)

$$\left\{\begin{matrix}m=\frac{20x^{2}-280x+981}{20no\left(x+6\right)x^{2}}\text{, }&x\neq 0\text{ and }o\neq 0\text{ and }x\neq -6\text{ and }n\neq 0\\m\in \mathrm{C}\text{, }&\left(x=\frac{\sqrt{5}i}{10}+7\text{ and }n=0\right)\text{ or }\left(x=\frac{\sqrt{5}i}{10}+7\text{ and }o=0\right)\text{ or }\left(x=-\frac{\sqrt{5}i}{10}+7\text{ and }n=0\right)\text{ or }\left(x=-\frac{\sqrt{5}i}{10}+7\text{ and }o=0\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te x ki te x, ka x^{2}.

$$\left(x-7\right)^{2}-x^{2}\left(6+x\right)mon=-\frac{1}{20}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-7\right)^{2}.

$$x^{2}-14x+49-x^{2}\left(6+x\right)mon=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2} ki te 6+x.

$$x^{2}-14x+49-\left(6x^{2}+x^{3}\right)mon=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}+x^{3} ki te m.

$$x^{2}-14x+49-\left(6x^{2}m+x^{3}m\right)on=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}m+x^{3}m ki te o.

$$x^{2}-14x+49-\left(6x^{2}mo+x^{3}mo\right)n=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}mo+x^{3}mo ki te n.

$$x^{2}-14x+49-\left(6x^{2}mon+x^{3}mon\right)=-\frac{1}{20}$$

Hei kimi i te tauaro o 6x^{2}mon+x^{3}mon, kimihia te tauaro o ia taurangi.

$$x^{2}-14x+49-6x^{2}mon-x^{3}mon=-\frac{1}{20}$$

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

$$-14x+49-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}$$

Me tāpiri te 14x ki ngā taha e rua.

$$49-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}+14x$$

Tangohia te 49 mai i ngā taha e rua.

$$-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}+14x-49$$

Tangohia te 49 i te -\frac{1}{20}, ka -\frac{981}{20}.

$$-6x^{2}mon-x^{3}mon=-\frac{981}{20}-x^{2}+14x$$

Pahekotia ngā kīanga tau katoa e whai ana i te m.

$$\left(-6x^{2}on-x^{3}on\right)m=-\frac{981}{20}-x^{2}+14x$$

He hanga arowhānui tō te whārite.

$$\left(-nox^{3}-6nox^{2}\right)m=-x^{2}+14x-\frac{981}{20}$$

Whakawehea ngā taha e rua ki te -6x^{2}on-x^{3}on.

$$\frac{\left(-nox^{3}-6nox^{2}\right)m}{-nox^{3}-6nox^{2}}=\frac{-x^{2}+14x-\frac{981}{20}}{-nox^{3}-6nox^{2}}$$

Mā te whakawehe ki te -6x^{2}on-x^{3}on ka wetekia te whakareanga ki te -6x^{2}on-x^{3}on.

$$m=\frac{-x^{2}+14x-\frac{981}{20}}{-nox^{3}-6nox^{2}}$$

Whakawehe -x^{2}+14x-\frac{981}{20} ki te -6x^{2}on-x^{3}on.

$$m=-\frac{-20x^{2}+280x-981}{20no\left(x+6\right)x^{2}}$$

Whakaoti mō n (complex solution)

$$\left\{\begin{matrix}n=\frac{20x^{2}-280x+981}{20mo\left(x+6\right)x^{2}}\text{, }&x\neq 0\text{ and }o\neq 0\text{ and }x\neq -6\text{ and }m\neq 0\\n\in \mathrm{C}\text{, }&\left(x=\frac{\sqrt{5}i}{10}+7\text{ and }m=0\right)\text{ or }\left(x=\frac{\sqrt{5}i}{10}+7\text{ and }o=0\right)\text{ or }\left(x=-\frac{\sqrt{5}i}{10}+7\text{ and }m=0\right)\text{ or }\left(x=-\frac{\sqrt{5}i}{10}+7\text{ and }o=0\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te x ki te x, ka x^{2}.

$$\left(x-7\right)^{2}-x^{2}\left(6+x\right)mon=-\frac{1}{20}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-7\right)^{2}.

$$x^{2}-14x+49-x^{2}\left(6+x\right)mon=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2} ki te 6+x.

$$x^{2}-14x+49-\left(6x^{2}+x^{3}\right)mon=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}+x^{3} ki te m.

$$x^{2}-14x+49-\left(6x^{2}m+x^{3}m\right)on=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}m+x^{3}m ki te o.

$$x^{2}-14x+49-\left(6x^{2}mo+x^{3}mo\right)n=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}mo+x^{3}mo ki te n.

$$x^{2}-14x+49-\left(6x^{2}mon+x^{3}mon\right)=-\frac{1}{20}$$

Hei kimi i te tauaro o 6x^{2}mon+x^{3}mon, kimihia te tauaro o ia taurangi.

$$x^{2}-14x+49-6x^{2}mon-x^{3}mon=-\frac{1}{20}$$

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

$$-14x+49-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}$$

Me tāpiri te 14x ki ngā taha e rua.

$$49-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}+14x$$

Tangohia te 49 mai i ngā taha e rua.

$$-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}+14x-49$$

Tangohia te 49 i te -\frac{1}{20}, ka -\frac{981}{20}.

$$-6x^{2}mon-x^{3}mon=-\frac{981}{20}-x^{2}+14x$$

Pahekotia ngā kīanga tau katoa e whai ana i te n.

$$\left(-6x^{2}mo-x^{3}mo\right)n=-\frac{981}{20}-x^{2}+14x$$

He hanga arowhānui tō te whārite.

$$\left(-mox^{3}-6mox^{2}\right)n=-x^{2}+14x-\frac{981}{20}$$

Whakawehea ngā taha e rua ki te -6x^{2}mo-x^{3}mo.

$$\frac{\left(-mox^{3}-6mox^{2}\right)n}{-mox^{3}-6mox^{2}}=\frac{-x^{2}+14x-\frac{981}{20}}{-mox^{3}-6mox^{2}}$$

Mā te whakawehe ki te -6x^{2}mo-x^{3}mo ka wetekia te whakareanga ki te -6x^{2}mo-x^{3}mo.

$$n=\frac{-x^{2}+14x-\frac{981}{20}}{-mox^{3}-6mox^{2}}$$

Whakawehe -x^{2}+14x-\frac{981}{20} ki te -6x^{2}mo-x^{3}mo.

$$n=-\frac{-20x^{2}+280x-981}{20mo\left(x+6\right)x^{2}}$$

Whakaoti mō m

$$m=\frac{20x^{2}-280x+981}{20no\left(x+6\right)x^{2}}$$

$$x\neq 0\text{ and }o\neq 0\text{ and }x\neq -6\text{ and }n\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te x ki te x, ka x^{2}.

$$\left(x-7\right)^{2}-x^{2}\left(6+x\right)mon=-\frac{1}{20}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-7\right)^{2}.

$$x^{2}-14x+49-x^{2}\left(6+x\right)mon=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2} ki te 6+x.

$$x^{2}-14x+49-\left(6x^{2}+x^{3}\right)mon=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}+x^{3} ki te m.

$$x^{2}-14x+49-\left(6x^{2}m+x^{3}m\right)on=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}m+x^{3}m ki te o.

$$x^{2}-14x+49-\left(6x^{2}mo+x^{3}mo\right)n=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}mo+x^{3}mo ki te n.

$$x^{2}-14x+49-\left(6x^{2}mon+x^{3}mon\right)=-\frac{1}{20}$$

Hei kimi i te tauaro o 6x^{2}mon+x^{3}mon, kimihia te tauaro o ia taurangi.

$$x^{2}-14x+49-6x^{2}mon-x^{3}mon=-\frac{1}{20}$$

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

$$-14x+49-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}$$

Me tāpiri te 14x ki ngā taha e rua.

$$49-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}+14x$$

Tangohia te 49 mai i ngā taha e rua.

$$-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}+14x-49$$

Tangohia te 49 i te -\frac{1}{20}, ka -\frac{981}{20}.

$$-6x^{2}mon-x^{3}mon=-\frac{981}{20}-x^{2}+14x$$

Pahekotia ngā kīanga tau katoa e whai ana i te m.

$$\left(-6x^{2}on-x^{3}on\right)m=-\frac{981}{20}-x^{2}+14x$$

He hanga arowhānui tō te whārite.

$$\left(-nox^{3}-6nox^{2}\right)m=-x^{2}+14x-\frac{981}{20}$$

Whakawehea ngā taha e rua ki te -6x^{2}on-x^{3}on.

$$\frac{\left(-nox^{3}-6nox^{2}\right)m}{-nox^{3}-6nox^{2}}=\frac{-x^{2}+14x-\frac{981}{20}}{-nox^{3}-6nox^{2}}$$

Mā te whakawehe ki te -6x^{2}on-x^{3}on ka wetekia te whakareanga ki te -6x^{2}on-x^{3}on.

$$m=\frac{-x^{2}+14x-\frac{981}{20}}{-nox^{3}-6nox^{2}}$$

Whakawehe -\frac{981}{20}-x^{2}+14x ki te -6x^{2}on-x^{3}on.

$$m=\frac{-20x^{2}+280x-981}{-20no\left(x+6\right)x^{2}}$$

Whakaoti mō n

$$n=\frac{20x^{2}-280x+981}{20mo\left(x+6\right)x^{2}}$$

$$x\neq 0\text{ and }o\neq 0\text{ and }x\neq -6\text{ and }m\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te x ki te x, ka x^{2}.

$$\left(x-7\right)^{2}-x^{2}\left(6+x\right)mon=-\frac{1}{20}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-7\right)^{2}.

$$x^{2}-14x+49-x^{2}\left(6+x\right)mon=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2} ki te 6+x.

$$x^{2}-14x+49-\left(6x^{2}+x^{3}\right)mon=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}+x^{3} ki te m.

$$x^{2}-14x+49-\left(6x^{2}m+x^{3}m\right)on=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}m+x^{3}m ki te o.

$$x^{2}-14x+49-\left(6x^{2}mo+x^{3}mo\right)n=-\frac{1}{20}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}mo+x^{3}mo ki te n.

$$x^{2}-14x+49-\left(6x^{2}mon+x^{3}mon\right)=-\frac{1}{20}$$

Hei kimi i te tauaro o 6x^{2}mon+x^{3}mon, kimihia te tauaro o ia taurangi.

$$x^{2}-14x+49-6x^{2}mon-x^{3}mon=-\frac{1}{20}$$

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

$$-14x+49-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}$$

Me tāpiri te 14x ki ngā taha e rua.

$$49-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}+14x$$

Tangohia te 49 mai i ngā taha e rua.

$$-6x^{2}mon-x^{3}mon=-\frac{1}{20}-x^{2}+14x-49$$

Tangohia te 49 i te -\frac{1}{20}, ka -\frac{981}{20}.

$$-6x^{2}mon-x^{3}mon=-\frac{981}{20}-x^{2}+14x$$

Pahekotia ngā kīanga tau katoa e whai ana i te n.

$$\left(-6x^{2}mo-x^{3}mo\right)n=-\frac{981}{20}-x^{2}+14x$$

He hanga arowhānui tō te whārite.

$$\left(-mox^{3}-6mox^{2}\right)n=-x^{2}+14x-\frac{981}{20}$$

Whakawehea ngā taha e rua ki te -6x^{2}mo-x^{3}mo.

$$\frac{\left(-mox^{3}-6mox^{2}\right)n}{-mox^{3}-6mox^{2}}=\frac{-x^{2}+14x-\frac{981}{20}}{-mox^{3}-6mox^{2}}$$

Mā te whakawehe ki te -6x^{2}mo-x^{3}mo ka wetekia te whakareanga ki te -6x^{2}mo-x^{3}mo.

$$n=\frac{-x^{2}+14x-\frac{981}{20}}{-mox^{3}-6mox^{2}}$$

Whakawehe -\frac{981}{20}-x^{2}+14x ki te -6x^{2}mo-x^{3}mo.

$$n=\frac{-20x^{2}+280x-981}{-20mo\left(x+6\right)x^{2}}$$