Whakaoti i te (-01-01)^2+(200-y)-(-115+4)^2=18225

$$( - 01 - 01 ) ^ { 2 } + \{ ( 200 - y ) - ( - 115 + 4 ) \} ^ { 2 } = 18225$$

Whakaoti mō y

$$y=176$$

$$y=446$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 1, ka 0.

$$\left(0-0\times 1\right)^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

Whakareatia te 0 ki te 1, ka 0.

$$\left(0-0\right)^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

Mā te tango i te 0 i a ia ake anō ka toe ko te 0.

$$0^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

Tātaihia te 0 mā te pū o 2, kia riro ko 0.

$$0+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

Tāpirihia te -115 ki te 4, ka -111.

$$0+\left(200-y-\left(-111\right)\right)^{2}=18225$$

Ko te tauaro o -111 ko 111.

$$0+\left(200-y+111\right)^{2}=18225$$

Pūrua 200-y+111.

$$0+y^{2}-622y+96721=18225$$

Tāpirihia te 0 ki te 96721, ka 96721.

$$96721+y^{2}-622y=18225$$

Tangohia te 18225 mai i ngā taha e rua.

$$96721+y^{2}-622y-18225=0$$

Tangohia te 18225 i te 96721, ka 78496.

$$78496+y^{2}-622y=0$$

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.

$$y^{2}-622y+78496=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -622 mō b, me 78496 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-622\right)±\sqrt{\left(-622\right)^{2}-4\times 78496}}{2}$$

Pūrua -622.

$$y=\frac{-\left(-622\right)±\sqrt{386884-4\times 78496}}{2}$$

Whakareatia -4 ki te 78496.

$$y=\frac{-\left(-622\right)±\sqrt{386884-313984}}{2}$$

Tāpiri 386884 ki te -313984.

$$y=\frac{-\left(-622\right)±\sqrt{72900}}{2}$$

Tuhia te pūtakerua o te 72900.

$$y=\frac{-\left(-622\right)±270}{2}$$

Ko te tauaro o -622 ko 622.

$$y=\frac{622±270}{2}$$

Nā, me whakaoti te whārite y=\frac{622±270}{2} ina he tāpiri te ±. Tāpiri 622 ki te 270.

$$y=\frac{892}{2}$$

Whakawehe 892 ki te 2.

$$y=446$$

Nā, me whakaoti te whārite y=\frac{622±270}{2} ina he tango te ±. Tango 270 mai i 622.

$$y=\frac{352}{2}$$

Whakawehe 352 ki te 2.

$$y=176$$

Kua oti te whārite te whakatau.

$$y=446 y=176$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 0 ki te 1, ka 0.

$$\left(0-0\times 1\right)^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

Whakareatia te 0 ki te 1, ka 0.

$$\left(0-0\right)^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

Mā te tango i te 0 i a ia ake anō ka toe ko te 0.

$$0^{2}+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

Tātaihia te 0 mā te pū o 2, kia riro ko 0.

$$0+\left(200-y-\left(-115+4\right)\right)^{2}=18225$$

Tāpirihia te -115 ki te 4, ka -111.

$$0+\left(200-y-\left(-111\right)\right)^{2}=18225$$

Ko te tauaro o -111 ko 111.

$$0+\left(200-y+111\right)^{2}=18225$$

Pūrua 200-y+111.

$$0+y^{2}-622y+96721=18225$$

Tāpirihia te 0 ki te 96721, ka 96721.

$$96721+y^{2}-622y=18225$$

Tangohia te 96721 mai i ngā taha e rua.

$$y^{2}-622y=18225-96721$$

Tangohia te 96721 i te 18225, ka -78496.

$$y^{2}-622y=-78496$$

Whakawehea te -622, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -311. Nā, tāpiria te pūrua o te -311 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$y^{2}-622y+\left(-311\right)^{2}=-78496+\left(-311\right)^{2}$$

Pūrua -311.

$$y^{2}-622y+96721=-78496+96721$$

Tāpiri -78496 ki te 96721.

$$y^{2}-622y+96721=18225$$

Tauwehea y^{2}-622y+96721. 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}.

$$\left(y-311\right)^{2}=18225$$

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

$$\sqrt{\left(y-311\right)^{2}}=\sqrt{18225}$$

Whakarūnātia.

$$y-311=135 y-311=-135$$

Me tāpiri 311 ki ngā taha e rua o te whārite.

$$y=446 y=176$$