Whakaoti i te +54x+sqrt{x}=75

$$+54x+ \sqrt{ x } = 75$$

Whakaoti mō x

$$x = \frac{8101 - \sqrt{16201}}{5832} \approx 1.3672354$$

Ngā Upane Otinga

Me tango 54x mai i ngā taha e rua o te whārite.

$$\sqrt{x}=75-54x$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x}\right)^{2}=\left(75-54x\right)^{2}$$

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

$$x=\left(75-54x\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(75-54x\right)^{2}.

$$x=5625-8100x+2916x^{2}$$

Tangohia te 5625 mai i ngā taha e rua.

$$x-5625=-8100x+2916x^{2}$$

Me tāpiri te 8100x ki ngā taha e rua.

$$x-5625+8100x=2916x^{2}$$

Pahekotia te x me 8100x, ka 8101x.

$$8101x-5625=2916x^{2}$$

Tangohia te 2916x^{2} mai i ngā taha e rua.

$$8101x-5625-2916x^{2}=0$$

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.

$$-2916x^{2}+8101x-5625=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2916 mō a, 8101 mō b, me -5625 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8101±\sqrt{8101^{2}-4\left(-2916\right)\left(-5625\right)}}{2\left(-2916\right)}$$

Pūrua 8101.

$$x=\frac{-8101±\sqrt{65626201-4\left(-2916\right)\left(-5625\right)}}{2\left(-2916\right)}$$

Whakareatia -4 ki te -2916.

$$x=\frac{-8101±\sqrt{65626201+11664\left(-5625\right)}}{2\left(-2916\right)}$$

Whakareatia 11664 ki te -5625.

$$x=\frac{-8101±\sqrt{65626201-65610000}}{2\left(-2916\right)}$$

Tāpiri 65626201 ki te -65610000.

$$x=\frac{-8101±\sqrt{16201}}{2\left(-2916\right)}$$

Whakareatia 2 ki te -2916.

$$x=\frac{-8101±\sqrt{16201}}{-5832}$$

Nā, me whakaoti te whārite x=\frac{-8101±\sqrt{16201}}{-5832} ina he tāpiri te ±. Tāpiri -8101 ki te \sqrt{16201}.

$$x=\frac{\sqrt{16201}-8101}{-5832}$$

Whakawehe -8101+\sqrt{16201} ki te -5832.

$$x=\frac{8101-\sqrt{16201}}{5832}$$

Nā, me whakaoti te whārite x=\frac{-8101±\sqrt{16201}}{-5832} ina he tango te ±. Tango \sqrt{16201} mai i -8101.

$$x=\frac{-\sqrt{16201}-8101}{-5832}$$

Whakawehe -8101-\sqrt{16201} ki te -5832.

$$x=\frac{\sqrt{16201}+8101}{5832}$$

Kua oti te whārite te whakatau.

$$x=\frac{8101-\sqrt{16201}}{5832} x=\frac{\sqrt{16201}+8101}{5832}$$

Whakakapia te \frac{8101-\sqrt{16201}}{5832} mō te x i te whārite 54x+\sqrt{x}=75.

$$54\times \frac{8101-\sqrt{16201}}{5832}+\sqrt{\frac{8101-\sqrt{16201}}{5832}}=75$$

Whakarūnātia. Ko te uara x=\frac{8101-\sqrt{16201}}{5832} kua ngata te whārite.

$$75=75$$

Whakakapia te \frac{\sqrt{16201}+8101}{5832} mō te x i te whārite 54x+\sqrt{x}=75.

$$54\times \frac{\sqrt{16201}+8101}{5832}+\sqrt{\frac{\sqrt{16201}+8101}{5832}}=75$$

Whakarūnātia. Ko te uara x=\frac{\sqrt{16201}+8101}{5832} kāore e ngata ana ki te whārite.

$$\frac{1}{54}\times 16201^{\frac{1}{2}}+\frac{4051}{54}=75$$

Ko te whārite \sqrt{x}=75-54x he rongoā ahurei.

$$x=\frac{8101-\sqrt{16201}}{5832}$$