Whakaoti i te x=-1018-9000/x

$$x=-1018- \frac{ 9000 }{ x }$$

Whakaoti mō x (complex solution)

$$x=\sqrt{250081}-509\approx -8.91900656$$

$$x=-\left(\sqrt{250081}+509\right)\approx -1009.08099344$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia -1018 ki te \frac{x}{x}.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

Tā te mea he rite te tauraro o -\frac{1018x}{x} me \frac{9000}{x}, me tango rāua mā te tango i ō raua taurunga.

$$x=\frac{-1018x-9000}{x}$$

Tangohia te \frac{-1018x-9000}{x} mai i ngā taha e rua.

$$x-\frac{-1018x-9000}{x}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{x}{x}.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

Tā te mea he rite te tauraro o \frac{xx}{x} me \frac{-1018x-9000}{x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

Mahia ngā whakarea i roto o xx-\left(-1018x-9000\right).

$$\frac{x^{2}+1018x+9000}{x}=0$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$x^{2}+1018x+9000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 1018 mō b, me 9000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1018±\sqrt{1018^{2}-4\times 9000}}{2}$$

Pūrua 1018.

$$x=\frac{-1018±\sqrt{1036324-4\times 9000}}{2}$$

Whakareatia -4 ki te 9000.

$$x=\frac{-1018±\sqrt{1036324-36000}}{2}$$

Tāpiri 1036324 ki te -36000.

$$x=\frac{-1018±\sqrt{1000324}}{2}$$

Tuhia te pūtakerua o te 1000324.

$$x=\frac{-1018±2\sqrt{250081}}{2}$$

Nā, me whakaoti te whārite x=\frac{-1018±2\sqrt{250081}}{2} ina he tāpiri te ±. Tāpiri -1018 ki te 2\sqrt{250081}.

$$x=\frac{2\sqrt{250081}-1018}{2}$$

Whakawehe -1018+2\sqrt{250081} ki te 2.

$$x=\sqrt{250081}-509$$

Nā, me whakaoti te whārite x=\frac{-1018±2\sqrt{250081}}{2} ina he tango te ±. Tango 2\sqrt{250081} mai i -1018.

$$x=\frac{-2\sqrt{250081}-1018}{2}$$

Whakawehe -1018-2\sqrt{250081} ki te 2.

$$x=-\sqrt{250081}-509$$

Kua oti te whārite te whakatau.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$

Ngā Upane mō te Whakaoti i te Pūrua

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia -1018 ki te \frac{x}{x}.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

Tā te mea he rite te tauraro o -\frac{1018x}{x} me \frac{9000}{x}, me tango rāua mā te tango i ō raua taurunga.

$$x=\frac{-1018x-9000}{x}$$

Tangohia te \frac{-1018x-9000}{x} mai i ngā taha e rua.

$$x-\frac{-1018x-9000}{x}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{x}{x}.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

Tā te mea he rite te tauraro o \frac{xx}{x} me \frac{-1018x-9000}{x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

Mahia ngā whakarea i roto o xx-\left(-1018x-9000\right).

$$\frac{x^{2}+1018x+9000}{x}=0$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$x^{2}+1018x+9000=0$$

Tangohia te 9000 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}+1018x=-9000$$

Whakawehea te 1018, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 509. Nā, tāpiria te pūrua o te 509 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+1018x+509^{2}=-9000+509^{2}$$

Pūrua 509.

$$x^{2}+1018x+259081=-9000+259081$$

Tāpiri -9000 ki te 259081.

$$x^{2}+1018x+259081=250081$$

Tauwehea x^{2}+1018x+259081. 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}.

$$\left(x+509\right)^{2}=250081$$

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

$$\sqrt{\left(x+509\right)^{2}}=\sqrt{250081}$$

Whakarūnātia.

$$x+509=\sqrt{250081} x+509=-\sqrt{250081}$$

Me tango 509 mai i ngā taha e rua o te whārite.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$

Whakaoti mō x

$$x=\sqrt{250081}-509\approx -8.91900656$$

$$x=-\sqrt{250081}-509\approx -1009.08099344$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia -1018 ki te \frac{x}{x}.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

Tā te mea he rite te tauraro o -\frac{1018x}{x} me \frac{9000}{x}, me tango rāua mā te tango i ō raua taurunga.

$$x=\frac{-1018x-9000}{x}$$

Tangohia te \frac{-1018x-9000}{x} mai i ngā taha e rua.

$$x-\frac{-1018x-9000}{x}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{x}{x}.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

Tā te mea he rite te tauraro o \frac{xx}{x} me \frac{-1018x-9000}{x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

Mahia ngā whakarea i roto o xx-\left(-1018x-9000\right).

$$\frac{x^{2}+1018x+9000}{x}=0$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$x^{2}+1018x+9000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 1018 mō b, me 9000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1018±\sqrt{1018^{2}-4\times 9000}}{2}$$

Pūrua 1018.

$$x=\frac{-1018±\sqrt{1036324-4\times 9000}}{2}$$

Whakareatia -4 ki te 9000.

$$x=\frac{-1018±\sqrt{1036324-36000}}{2}$$

Tāpiri 1036324 ki te -36000.

$$x=\frac{-1018±\sqrt{1000324}}{2}$$

Tuhia te pūtakerua o te 1000324.

$$x=\frac{-1018±2\sqrt{250081}}{2}$$

Nā, me whakaoti te whārite x=\frac{-1018±2\sqrt{250081}}{2} ina he tāpiri te ±. Tāpiri -1018 ki te 2\sqrt{250081}.

$$x=\frac{2\sqrt{250081}-1018}{2}$$

Whakawehe -1018+2\sqrt{250081} ki te 2.

$$x=\sqrt{250081}-509$$

Nā, me whakaoti te whārite x=\frac{-1018±2\sqrt{250081}}{2} ina he tango te ±. Tango 2\sqrt{250081} mai i -1018.

$$x=\frac{-2\sqrt{250081}-1018}{2}$$

Whakawehe -1018-2\sqrt{250081} ki te 2.

$$x=-\sqrt{250081}-509$$

Kua oti te whārite te whakatau.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$

Ngā Upane mō te Whakaoti i te Pūrua

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia -1018 ki te \frac{x}{x}.

$$x=-\frac{1018x}{x}-\frac{9000}{x}$$

Tā te mea he rite te tauraro o -\frac{1018x}{x} me \frac{9000}{x}, me tango rāua mā te tango i ō raua taurunga.

$$x=\frac{-1018x-9000}{x}$$

Tangohia te \frac{-1018x-9000}{x} mai i ngā taha e rua.

$$x-\frac{-1018x-9000}{x}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{x}{x}.

$$\frac{xx}{x}-\frac{-1018x-9000}{x}=0$$

Tā te mea he rite te tauraro o \frac{xx}{x} me \frac{-1018x-9000}{x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{xx-\left(-1018x-9000\right)}{x}=0$$

Mahia ngā whakarea i roto o xx-\left(-1018x-9000\right).

$$\frac{x^{2}+1018x+9000}{x}=0$$

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$x^{2}+1018x+9000=0$$

Tangohia te 9000 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}+1018x=-9000$$

Whakawehea te 1018, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 509. Nā, tāpiria te pūrua o te 509 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+1018x+509^{2}=-9000+509^{2}$$

Pūrua 509.

$$x^{2}+1018x+259081=-9000+259081$$

Tāpiri -9000 ki te 259081.

$$x^{2}+1018x+259081=250081$$

Tauwehea x^{2}+1018x+259081. 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}.

$$\left(x+509\right)^{2}=250081$$

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

$$\sqrt{\left(x+509\right)^{2}}=\sqrt{250081}$$

Whakarūnātia.

$$x+509=\sqrt{250081} x+509=-\sqrt{250081}$$

Me tango 509 mai i ngā taha e rua o te whārite.

$$x=\sqrt{250081}-509 x=-\sqrt{250081}-509$$