Whakaoti i te x+120*66/1266-x=76

$$x + \frac { 120 \times 66 } { 1266 - x } = 76$$

Whakaoti mō x

$$x=\sqrt{361945}+671\approx 1272.618649977$$

$$x=671-\sqrt{361945}\approx 69.381350023$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 1266 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+1266.

$$\left(-x+1266\right)x+120\times 66=76\left(-x+1266\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -x+1266 ki te x.

$$-x^{2}+1266x+120\times 66=76\left(-x+1266\right)$$

Whakareatia te 120 ki te 66, ka 7920.

$$-x^{2}+1266x+7920=76\left(-x+1266\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 76 ki te -x+1266.

$$-x^{2}+1266x+7920=-76x+96216$$

Me tāpiri te 76x ki ngā taha e rua.

$$-x^{2}+1266x+7920+76x=96216$$

Pahekotia te 1266x me 76x, ka 1342x.

$$-x^{2}+1342x+7920=96216$$

Tangohia te 96216 mai i ngā taha e rua.

$$-x^{2}+1342x+7920-96216=0$$

Tangohia te 96216 i te 7920, ka -88296.

$$-x^{2}+1342x-88296=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 1342 mō b, me -88296 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1342±\sqrt{1342^{2}-4\left(-1\right)\left(-88296\right)}}{2\left(-1\right)}$$

Pūrua 1342.

$$x=\frac{-1342±\sqrt{1800964-4\left(-1\right)\left(-88296\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-1342±\sqrt{1800964+4\left(-88296\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -88296.

$$x=\frac{-1342±\sqrt{1800964-353184}}{2\left(-1\right)}$$

Tāpiri 1800964 ki te -353184.

$$x=\frac{-1342±\sqrt{1447780}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 1447780.

$$x=\frac{-1342±2\sqrt{361945}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-1342±2\sqrt{361945}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-1342±2\sqrt{361945}}{-2} ina he tāpiri te ±. Tāpiri -1342 ki te 2\sqrt{361945}.

$$x=\frac{2\sqrt{361945}-1342}{-2}$$

Whakawehe -1342+2\sqrt{361945} ki te -2.

$$x=671-\sqrt{361945}$$

Nā, me whakaoti te whārite x=\frac{-1342±2\sqrt{361945}}{-2} ina he tango te ±. Tango 2\sqrt{361945} mai i -1342.

$$x=\frac{-2\sqrt{361945}-1342}{-2}$$

Whakawehe -1342-2\sqrt{361945} ki te -2.

$$x=\sqrt{361945}+671$$

Kua oti te whārite te whakatau.

$$x=671-\sqrt{361945} x=\sqrt{361945}+671$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 1266 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+1266.

$$\left(-x+1266\right)x+120\times 66=76\left(-x+1266\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -x+1266 ki te x.

$$-x^{2}+1266x+120\times 66=76\left(-x+1266\right)$$

Whakareatia te 120 ki te 66, ka 7920.

$$-x^{2}+1266x+7920=76\left(-x+1266\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 76 ki te -x+1266.

$$-x^{2}+1266x+7920=-76x+96216$$

Me tāpiri te 76x ki ngā taha e rua.

$$-x^{2}+1266x+7920+76x=96216$$

Pahekotia te 1266x me 76x, ka 1342x.

$$-x^{2}+1342x+7920=96216$$

Tangohia te 7920 mai i ngā taha e rua.

$$-x^{2}+1342x=96216-7920$$

Tangohia te 7920 i te 96216, ka 88296.

$$-x^{2}+1342x=88296$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+1342x}{-1}=\frac{88296}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{1342}{-1}x=\frac{88296}{-1}$$

Whakawehe 1342 ki te -1.

$$x^{2}-1342x=\frac{88296}{-1}$$

Whakawehe 88296 ki te -1.

$$x^{2}-1342x=-88296$$

Whakawehea te -1342, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -671. Nā, tāpiria te pūrua o te -671 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-1342x+\left(-671\right)^{2}=-88296+\left(-671\right)^{2}$$

Pūrua -671.

$$x^{2}-1342x+450241=-88296+450241$$

Tāpiri -88296 ki te 450241.

$$x^{2}-1342x+450241=361945$$

Tauwehea x^{2}-1342x+450241. 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}.

$$\left(x-671\right)^{2}=361945$$

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

$$\sqrt{\left(x-671\right)^{2}}=\sqrt{361945}$$

Whakarūnātia.

$$x-671=\sqrt{361945} x-671=-\sqrt{361945}$$

Me tāpiri 671 ki ngā taha e rua o te whārite.

$$x=\sqrt{361945}+671 x=671-\sqrt{361945}$$