Whakaoti i te 2c-17=sqrt{-121+13c}

$$2 c - 17 = \sqrt { - 121 + 13 c }$$

Whakaoti mō c

$$c = \frac{41}{4} = 10\frac{1}{4} = 10.25$$

$$c=10$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(2c-17\right)^{2}=\left(\sqrt{-121+13c}\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2c-17\right)^{2}.

$$4c^{2}-68c+289=\left(\sqrt{-121+13c}\right)^{2}$$

Tātaihia te \sqrt{-121+13c} mā te pū o 2, kia riro ko -121+13c.

$$4c^{2}-68c+289=-121+13c$$

Tangohia te -121 mai i ngā taha e rua.

$$4c^{2}-68c+289-\left(-121\right)=13c$$

Ko te tauaro o -121 ko 121.

$$4c^{2}-68c+289+121=13c$$

Tangohia te 13c mai i ngā taha e rua.

$$4c^{2}-68c+289+121-13c=0$$

Tāpirihia te 289 ki te 121, ka 410.

$$4c^{2}-68c+410-13c=0$$

Pahekotia te -68c me -13c, ka -81c.

$$4c^{2}-81c+410=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, -81 mō b, me 410 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{-\left(-81\right)±\sqrt{\left(-81\right)^{2}-4\times 4\times 410}}{2\times 4}$$

Pūrua -81.

$$c=\frac{-\left(-81\right)±\sqrt{6561-4\times 4\times 410}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$c=\frac{-\left(-81\right)±\sqrt{6561-16\times 410}}{2\times 4}$$

Whakareatia -16 ki te 410.

$$c=\frac{-\left(-81\right)±\sqrt{6561-6560}}{2\times 4}$$

Tāpiri 6561 ki te -6560.

$$c=\frac{-\left(-81\right)±\sqrt{1}}{2\times 4}$$

Tuhia te pūtakerua o te 1.

$$c=\frac{-\left(-81\right)±1}{2\times 4}$$

Ko te tauaro o -81 ko 81.

$$c=\frac{81±1}{2\times 4}$$

Whakareatia 2 ki te 4.

$$c=\frac{81±1}{8}$$

Nā, me whakaoti te whārite c=\frac{81±1}{8} ina he tāpiri te ±. Tāpiri 81 ki te 1.

$$c=\frac{82}{8}$$

Whakahekea te hautanga \frac{82}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$c=\frac{41}{4}$$

Nā, me whakaoti te whārite c=\frac{81±1}{8} ina he tango te ±. Tango 1 mai i 81.

$$c=\frac{80}{8}$$

Whakawehe 80 ki te 8.

$$c=10$$

Kua oti te whārite te whakatau.

$$c=\frac{41}{4} c=10$$

Whakakapia te \frac{41}{4} mō te c i te whārite 2c-17=\sqrt{-121+13c}.

$$2\times \frac{41}{4}-17=\sqrt{-121+13\times \frac{41}{4}}$$

Whakarūnātia. Ko te uara c=\frac{41}{4} kua ngata te whārite.

$$\frac{7}{2}=\frac{7}{2}$$

Whakakapia te 10 mō te c i te whārite 2c-17=\sqrt{-121+13c}.

$$2\times 10-17=\sqrt{-121+13\times 10}$$

Whakarūnātia. Ko te uara c=10 kua ngata te whārite.

$$3=3$$

Rārangihia ngā rongoā katoa o 2c-17=\sqrt{13c-121}.

$$c=\frac{41}{4} c=10$$