Whakaoti i te 0=0.16(h-8)^2

$$0 = 0.16 ( h - 8 ) ^ { 2 }$$

Whakaoti mō h

$$h=8$$

Ngā Upane Whakamahi Tauwehe

Whakawehea ngā taha e rua ki te 0.16. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$0=\left(h-8\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(h-8\right)^{2}.

$$0=h^{2}-16h+64$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$h^{2}-16h+64=0$$

Hei whakaoti i te whārite, whakatauwehea te h^{2}-16h+64 mā te whakamahi i te tātai h^{2}+\left(a+b\right)h+ab=\left(h+a\right)\left(h+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-16 ab=64$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 64.

$$-1,-64 -2,-32 -4,-16 -8,-8$$

Tātaihia te tapeke mō ia takirua.

$$-1-64=-65 -2-32=-34 -4-16=-20 -8-8=-16$$

Ko te otinga te takirua ka hoatu i te tapeke -16.

$$a=-8 b=-8$$

Me tuhi anō te kīanga whakatauwehe \left(h+a\right)\left(h+b\right) mā ngā uara i tātaihia.

$$\left(h-8\right)\left(h-8\right)$$

Tuhia anōtia hei pūrua huarua.

$$\left(h-8\right)^{2}$$

Hei kimi i te otinga whārite, whakaotia te h-8=0.

$$h=8$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakawehea ngā taha e rua ki te 0.16. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$0=\left(h-8\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(h-8\right)^{2}.

$$0=h^{2}-16h+64$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$h^{2}-16h+64=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei h^{2}+ah+bh+64. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-16 ab=1\times 64=64$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 64.

$$-1,-64 -2,-32 -4,-16 -8,-8$$

Tātaihia te tapeke mō ia takirua.

$$-1-64=-65 -2-32=-34 -4-16=-20 -8-8=-16$$

Ko te otinga te takirua ka hoatu i te tapeke -16.

$$a=-8 b=-8$$

Tuhia anō te h^{2}-16h+64 hei \left(h^{2}-8h\right)+\left(-8h+64\right).

$$\left(h^{2}-8h\right)+\left(-8h+64\right)$$

Tauwehea te h i te tuatahi me te -8 i te rōpū tuarua.

$$h\left(h-8\right)-8\left(h-8\right)$$

Whakatauwehea atu te kīanga pātahi h-8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(h-8\right)\left(h-8\right)$$

Tuhia anōtia hei pūrua huarua.

$$\left(h-8\right)^{2}$$

Hei kimi i te otinga whārite, whakaotia te h-8=0.

$$h=8$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ngā taha e rua ki te 0.16. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$0=\left(h-8\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(h-8\right)^{2}.

$$0=h^{2}-16h+64$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$h^{2}-16h+64=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -16 mō b, me 64 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 64}}{2}$$

Pūrua -16.

$$h=\frac{-\left(-16\right)±\sqrt{256-4\times 64}}{2}$$

Whakareatia -4 ki te 64.

$$h=\frac{-\left(-16\right)±\sqrt{256-256}}{2}$$

Tāpiri 256 ki te -256.

$$h=\frac{-\left(-16\right)±\sqrt{0}}{2}$$

Tuhia te pūtakerua o te 0.

$$h=-\frac{-16}{2}$$

Ko te tauaro o -16 ko 16.

$$h=\frac{16}{2}$$

Whakawehe 16 ki te 2.

$$h=8$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawehea ngā taha e rua ki te 0.16. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$0=\left(h-8\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(h-8\right)^{2}.

$$0=h^{2}-16h+64$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$h^{2}-16h+64=0$$

Tauwehea h^{2}-16h+64. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(h-8\right)^{2}=0$$

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

$$\sqrt{\left(h-8\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$h-8=0 h-8=0$$

Me tāpiri 8 ki ngā taha e rua o te whārite.

$$h=8 h=8$$

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

$$h=8$$