Whakaoti i te x+sqrt{x}=110

$$x+ \sqrt{ x } = 110$$

Whakaoti mō x

$$x=100$$

Ngā Upane Otinga

Me tango x mai i ngā taha e rua o te whārite.

$$\sqrt{x}=110-x$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x}\right)^{2}=\left(110-x\right)^{2}$$

Tātaihia te \sqrt{x} mā te pū o 2, kia riro ko x.

$$x=\left(110-x\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(110-x\right)^{2}.

$$x=12100-220x+x^{2}$$

Tangohia te 12100 mai i ngā taha e rua.

$$x-12100=-220x+x^{2}$$

Me tāpiri te 220x ki ngā taha e rua.

$$x-12100+220x=x^{2}$$

Pahekotia te x me 220x, ka 221x.

$$221x-12100=x^{2}$$

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

$$221x-12100-x^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-x^{2}+221x-12100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 221 mō b, me -12100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-221±\sqrt{221^{2}-4\left(-1\right)\left(-12100\right)}}{2\left(-1\right)}$$

Pūrua 221.

$$x=\frac{-221±\sqrt{48841-4\left(-1\right)\left(-12100\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-221±\sqrt{48841+4\left(-12100\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -12100.

$$x=\frac{-221±\sqrt{48841-48400}}{2\left(-1\right)}$$

Tāpiri 48841 ki te -48400.

$$x=\frac{-221±\sqrt{441}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 441.

$$x=\frac{-221±21}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-221±21}{-2}$$

Nā, me whakaoti te whārite x=\frac{-221±21}{-2} ina he tāpiri te ±. Tāpiri -221 ki te 21.

$$x=-\frac{200}{-2}$$

Whakawehe -200 ki te -2.

$$x=100$$

Nā, me whakaoti te whārite x=\frac{-221±21}{-2} ina he tango te ±. Tango 21 mai i -221.

$$x=-\frac{242}{-2}$$

Whakawehe -242 ki te -2.

$$x=121$$

Kua oti te whārite te whakatau.

$$x=100 x=121$$

Whakakapia te 100 mō te x i te whārite x+\sqrt{x}=110.

$$100+\sqrt{100}=110$$

Whakarūnātia. Ko te uara x=100 kua ngata te whārite.

$$110=110$$

Whakakapia te 121 mō te x i te whārite x+\sqrt{x}=110.

$$121+\sqrt{121}=110$$

Whakarūnātia. Ko te uara x=121 kāore e ngata ana ki te whārite.

$$132=110$$

Ko te whārite \sqrt{x}=110-x he rongoā ahurei.

$$x=100$$