Whakaoti i te 520div(x+10)+1=520+x

$$520 \div (x+10)+1=520+x$$

Whakaoti mō x

$$x=\frac{\sqrt{261161}-529}{2}\approx -8.980431278$$

$$x=\frac{-\sqrt{261161}-529}{2}\approx -520.019568722$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki -10 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+10.

$$520+x+10=\left(x+10\right)\times 520+\left(x+10\right)x$$

Tāpirihia te 520 ki te 10, ka 530.

$$530+x=\left(x+10\right)\times 520+\left(x+10\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+10 ki te 520.

$$530+x=520x+5200+\left(x+10\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+10 ki te x.

$$530+x=520x+5200+x^{2}+10x$$

Pahekotia te 520x me 10x, ka 530x.

$$530+x=530x+5200+x^{2}$$

Tangohia te 530x mai i ngā taha e rua.

$$530+x-530x=5200+x^{2}$$

Pahekotia te x me -530x, ka -529x.

$$530-529x=5200+x^{2}$$

Tangohia te 5200 mai i ngā taha e rua.

$$530-529x-5200=x^{2}$$

Tangohia te 5200 i te 530, ka -4670.

$$-4670-529x=x^{2}$$

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

$$-4670-529x-x^{2}=0$$

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.

$$-x^{2}-529x-4670=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -529 mō b, me -4670 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-529\right)±\sqrt{\left(-529\right)^{2}-4\left(-1\right)\left(-4670\right)}}{2\left(-1\right)}$$

Pūrua -529.

$$x=\frac{-\left(-529\right)±\sqrt{279841-4\left(-1\right)\left(-4670\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-529\right)±\sqrt{279841+4\left(-4670\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -4670.

$$x=\frac{-\left(-529\right)±\sqrt{279841-18680}}{2\left(-1\right)}$$

Tāpiri 279841 ki te -18680.

$$x=\frac{-\left(-529\right)±\sqrt{261161}}{2\left(-1\right)}$$

Ko te tauaro o -529 ko 529.

$$x=\frac{529±\sqrt{261161}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{529±\sqrt{261161}}{-2}$$

Nā, me whakaoti te whārite x=\frac{529±\sqrt{261161}}{-2} ina he tāpiri te ±. Tāpiri 529 ki te \sqrt{261161}.

$$x=\frac{\sqrt{261161}+529}{-2}$$

Whakawehe 529+\sqrt{261161} ki te -2.

$$x=\frac{-\sqrt{261161}-529}{2}$$

Nā, me whakaoti te whārite x=\frac{529±\sqrt{261161}}{-2} ina he tango te ±. Tango \sqrt{261161} mai i 529.

$$x=\frac{529-\sqrt{261161}}{-2}$$

Whakawehe 529-\sqrt{261161} ki te -2.

$$x=\frac{\sqrt{261161}-529}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{261161}-529}{2} x=\frac{\sqrt{261161}-529}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki -10 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+10.

$$520+x+10=\left(x+10\right)\times 520+\left(x+10\right)x$$

Tāpirihia te 520 ki te 10, ka 530.

$$530+x=\left(x+10\right)\times 520+\left(x+10\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+10 ki te 520.

$$530+x=520x+5200+\left(x+10\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+10 ki te x.

$$530+x=520x+5200+x^{2}+10x$$

Pahekotia te 520x me 10x, ka 530x.

$$530+x=530x+5200+x^{2}$$

Tangohia te 530x mai i ngā taha e rua.

$$530+x-530x=5200+x^{2}$$

Pahekotia te x me -530x, ka -529x.

$$530-529x=5200+x^{2}$$

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

$$530-529x-x^{2}=5200$$

Tangohia te 530 mai i ngā taha e rua.

$$-529x-x^{2}=5200-530$$

Tangohia te 530 i te 5200, ka 4670.

$$-529x-x^{2}=4670$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-x^{2}-529x=4670$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-529x}{-1}=\frac{4670}{-1}$$

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

$$x^{2}+\left(-\frac{529}{-1}\right)x=\frac{4670}{-1}$$

Whakawehe -529 ki te -1.

$$x^{2}+529x=\frac{4670}{-1}$$

Whakawehe 4670 ki te -1.

$$x^{2}+529x=-4670$$

Whakawehea te 529, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{529}{2}. Nā, tāpiria te pūrua o te \frac{529}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+529x+\left(\frac{529}{2}\right)^{2}=-4670+\left(\frac{529}{2}\right)^{2}$$

Pūruatia \frac{529}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+529x+\frac{279841}{4}=-4670+\frac{279841}{4}$$

Tāpiri -4670 ki te \frac{279841}{4}.

$$x^{2}+529x+\frac{279841}{4}=\frac{261161}{4}$$

Tauwehea x^{2}+529x+\frac{279841}{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}.

$$\left(x+\frac{529}{2}\right)^{2}=\frac{261161}{4}$$

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

$$\sqrt{\left(x+\frac{529}{2}\right)^{2}}=\sqrt{\frac{261161}{4}}$$

Whakarūnātia.

$$x+\frac{529}{2}=\frac{\sqrt{261161}}{2} x+\frac{529}{2}=-\frac{\sqrt{261161}}{2}$$

Me tango \frac{529}{2} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{261161}-529}{2} x=\frac{-\sqrt{261161}-529}{2}$$