Whakaoti i te 16/h+4=h/2

$$\frac { 16 } { h + 4 } = \frac { h } { 2 }$$

Whakaoti mō h

$$h=-8$$

$$h=4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe h ki -4 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2\left(h+4\right), arā, te tauraro pātahi he tino iti rawa te kitea o h+4,2.

$$2\times 16=\left(h+4\right)h$$

Whakareatia te 2 ki te 16, ka 32.

$$32=\left(h+4\right)h$$

Whakamahia te āhuatanga tohatoha hei whakarea te h+4 ki te h.

$$32=h^{2}+4h$$

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

$$h^{2}+4h=32$$

Tangohia te 32 mai i ngā taha e rua.

$$h^{2}+4h-32=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 4 mō b, me -32 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-4±\sqrt{4^{2}-4\left(-32\right)}}{2}$$

Pūrua 4.

$$h=\frac{-4±\sqrt{16-4\left(-32\right)}}{2}$$

Whakareatia -4 ki te -32.

$$h=\frac{-4±\sqrt{16+128}}{2}$$

Tāpiri 16 ki te 128.

$$h=\frac{-4±\sqrt{144}}{2}$$

Tuhia te pūtakerua o te 144.

$$h=\frac{-4±12}{2}$$

Nā, me whakaoti te whārite h=\frac{-4±12}{2} ina he tāpiri te ±. Tāpiri -4 ki te 12.

$$h=\frac{8}{2}$$

Whakawehe 8 ki te 2.

$$h=4$$

Nā, me whakaoti te whārite h=\frac{-4±12}{2} ina he tango te ±. Tango 12 mai i -4.

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

Whakawehe -16 ki te 2.

$$h=-8$$

Kua oti te whārite te whakatau.

$$h=4 h=-8$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe h ki -4 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 2\left(h+4\right), arā, te tauraro pātahi he tino iti rawa te kitea o h+4,2.

$$2\times 16=\left(h+4\right)h$$

Whakareatia te 2 ki te 16, ka 32.

$$32=\left(h+4\right)h$$

Whakamahia te āhuatanga tohatoha hei whakarea te h+4 ki te h.

$$32=h^{2}+4h$$

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

$$h^{2}+4h=32$$

Whakawehea te 4, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 2. Nā, tāpiria te pūrua o te 2 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$h^{2}+4h+2^{2}=32+2^{2}$$

Pūrua 2.

$$h^{2}+4h+4=32+4$$

Tāpiri 32 ki te 4.

$$h^{2}+4h+4=36$$

Tauwehea h^{2}+4h+4. 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}.

$$\left(h+2\right)^{2}=36$$

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

$$\sqrt{\left(h+2\right)^{2}}=\sqrt{36}$$

Whakarūnātia.

$$h+2=6 h+2=-6$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$h=4 h=-8$$