Whakaoti i te (x/2^3)^2-x(3x)+15(x/2)^2=x^2

$$( \frac { x } { 2 ^ { 3 } } ) ^ { 2 } - x ( 3 x ) + 15 ( \frac { x } { 2 } ) ^ { 2 } = x ^ { 2 }$$

Whakaoti mō x

$$x=0$$

Ngā Upane mā te Kimi Pūtakerua

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

$$\left(\frac{x}{2^{3}}\right)^{2}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Tātaihia te 2 mā te pū o 3, kia riro ko 8.

$$\left(\frac{x}{8}\right)^{2}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Kia whakarewa i te \frac{x}{8} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{x^{2}}{8^{2}}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x^{2}\times 3 ki te \frac{8^{2}}{8^{2}}.

$$\frac{x^{2}}{8^{2}}-\frac{x^{2}\times 3\times 8^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Tā te mea he rite te tauraro o \frac{x^{2}}{8^{2}} me \frac{x^{2}\times 3\times 8^{2}}{8^{2}}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x^{2}-x^{2}\times 3\times 8^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Mahia ngā whakarea i roto o x^{2}-x^{2}\times 3\times 8^{2}.

$$\frac{x^{2}-192x^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Whakakotahitia ngā kupu rite i x^{2}-192x^{2}.

$$\frac{-191x^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Kia whakarewa i te \frac{x}{2} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{-191x^{2}}{8^{2}}+15\times \frac{x^{2}}{2^{2}}=x^{2}$$

Tuhia te 15\times \frac{x^{2}}{2^{2}} hei hautanga kotahi.

$$\frac{-191x^{2}}{8^{2}}+\frac{15x^{2}}{2^{2}}=x^{2}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 8^{2} me 2^{2} ko 64. Whakareatia \frac{15x^{2}}{2^{2}} ki te \frac{16}{16}.

$$\frac{-191x^{2}}{64}+\frac{16\times 15x^{2}}{64}=x^{2}$$

Tā te mea he rite te tauraro o \frac{-191x^{2}}{64} me \frac{16\times 15x^{2}}{64}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-191x^{2}+16\times 15x^{2}}{64}=x^{2}$$

Mahia ngā whakarea i roto o -191x^{2}+16\times 15x^{2}.

$$\frac{-191x^{2}+240x^{2}}{64}=x^{2}$$

Whakakotahitia ngā kupu rite i -191x^{2}+240x^{2}.

$$\frac{49x^{2}}{64}=x^{2}$$

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

$$\frac{49x^{2}}{64}-x^{2}=0$$

Whakareatia ngā taha e rua o te whārite ki te 64.

$$49x^{2}-64x^{2}=0$$

Pahekotia te 49x^{2} me -64x^{2}, ka -15x^{2}.

$$-15x^{2}=0$$

Whakawehea ngā taha e rua ki te -15. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$x^{2}=0$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$x=0 x=0$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$\left(\frac{x}{2^{3}}\right)^{2}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Tātaihia te 2 mā te pū o 3, kia riro ko 8.

$$\left(\frac{x}{8}\right)^{2}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Kia whakarewa i te \frac{x}{8} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{x^{2}}{8^{2}}-x^{2}\times 3+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x^{2}\times 3 ki te \frac{8^{2}}{8^{2}}.

$$\frac{x^{2}}{8^{2}}-\frac{x^{2}\times 3\times 8^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Tā te mea he rite te tauraro o \frac{x^{2}}{8^{2}} me \frac{x^{2}\times 3\times 8^{2}}{8^{2}}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{x^{2}-x^{2}\times 3\times 8^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Mahia ngā whakarea i roto o x^{2}-x^{2}\times 3\times 8^{2}.

$$\frac{x^{2}-192x^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Whakakotahitia ngā kupu rite i x^{2}-192x^{2}.

$$\frac{-191x^{2}}{8^{2}}+15\times \left(\frac{x}{2}\right)^{2}=x^{2}$$

Kia whakarewa i te \frac{x}{2} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{-191x^{2}}{8^{2}}+15\times \frac{x^{2}}{2^{2}}=x^{2}$$

Tuhia te 15\times \frac{x^{2}}{2^{2}} hei hautanga kotahi.

$$\frac{-191x^{2}}{8^{2}}+\frac{15x^{2}}{2^{2}}=x^{2}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 8^{2} me 2^{2} ko 64. Whakareatia \frac{15x^{2}}{2^{2}} ki te \frac{16}{16}.

$$\frac{-191x^{2}}{64}+\frac{16\times 15x^{2}}{64}=x^{2}$$

Tā te mea he rite te tauraro o \frac{-191x^{2}}{64} me \frac{16\times 15x^{2}}{64}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-191x^{2}+16\times 15x^{2}}{64}=x^{2}$$

Mahia ngā whakarea i roto o -191x^{2}+16\times 15x^{2}.

$$\frac{-191x^{2}+240x^{2}}{64}=x^{2}$$

Whakakotahitia ngā kupu rite i -191x^{2}+240x^{2}.

$$\frac{49x^{2}}{64}=x^{2}$$

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

$$\frac{49x^{2}}{64}-x^{2}=0$$

Whakareatia ngā taha e rua o te whārite ki te 64.

$$49x^{2}-64x^{2}=0$$

Pahekotia te 49x^{2} me -64x^{2}, ka -15x^{2}.

$$-15x^{2}=0$$

Whakawehea ngā taha e rua ki te -15. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$x^{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Tuhia te pūtakerua o te 0^{2}.

$$x=\frac{0±0}{2}$$

Whakawehe 0 ki te 2.

$$x=0$$