Whakaoti i te (x(125x+15)-50*40)*30+x(125x+15)*100=6420000

$$(x(125x+15)-50 \times 40) \times 30+x(125x+15) \times 100=6420000$$

Whakaoti mō x

$$x=\frac{3\sqrt{18720169}}{650}-\frac{3}{50}\approx 19.909297203$$

$$x=-\frac{3\sqrt{18720169}}{650}-\frac{3}{50}\approx -20.029297203$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 125x+15.

$$\left(125x^{2}+15x-50\times 40\right)\times 30+x\left(125x+15\right)\times 100=6420000$$

Whakareatia te 50 ki te 40, ka 2000.

$$\left(125x^{2}+15x-2000\right)\times 30+x\left(125x+15\right)\times 100=6420000$$

Whakamahia te āhuatanga tohatoha hei whakarea te 125x^{2}+15x-2000 ki te 30.

$$3750x^{2}+450x-60000+x\left(125x+15\right)\times 100=6420000$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 125x+15.

$$3750x^{2}+450x-60000+\left(125x^{2}+15x\right)\times 100=6420000$$

Whakamahia te āhuatanga tohatoha hei whakarea te 125x^{2}+15x ki te 100.

$$3750x^{2}+450x-60000+12500x^{2}+1500x=6420000$$

Pahekotia te 3750x^{2} me 12500x^{2}, ka 16250x^{2}.

$$16250x^{2}+450x-60000+1500x=6420000$$

Pahekotia te 450x me 1500x, ka 1950x.

$$16250x^{2}+1950x-60000=6420000$$

Tangohia te 6420000 mai i ngā taha e rua.

$$16250x^{2}+1950x-60000-6420000=0$$

Tangohia te 6420000 i te -60000, ka -6480000.

$$16250x^{2}+1950x-6480000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 16250 mō a, 1950 mō b, me -6480000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1950±\sqrt{1950^{2}-4\times 16250\left(-6480000\right)}}{2\times 16250}$$

Pūrua 1950.

$$x=\frac{-1950±\sqrt{3802500-4\times 16250\left(-6480000\right)}}{2\times 16250}$$

Whakareatia -4 ki te 16250.

$$x=\frac{-1950±\sqrt{3802500-65000\left(-6480000\right)}}{2\times 16250}$$

Whakareatia -65000 ki te -6480000.

$$x=\frac{-1950±\sqrt{3802500+421200000000}}{2\times 16250}$$

Tāpiri 3802500 ki te 421200000000.

$$x=\frac{-1950±\sqrt{421203802500}}{2\times 16250}$$

Tuhia te pūtakerua o te 421203802500.

$$x=\frac{-1950±150\sqrt{18720169}}{2\times 16250}$$

Whakareatia 2 ki te 16250.

$$x=\frac{-1950±150\sqrt{18720169}}{32500}$$

Nā, me whakaoti te whārite x=\frac{-1950±150\sqrt{18720169}}{32500} ina he tāpiri te ±. Tāpiri -1950 ki te 150\sqrt{18720169}.

$$x=\frac{150\sqrt{18720169}-1950}{32500}$$

Whakawehe -1950+150\sqrt{18720169} ki te 32500.

$$x=\frac{3\sqrt{18720169}}{650}-\frac{3}{50}$$

Nā, me whakaoti te whārite x=\frac{-1950±150\sqrt{18720169}}{32500} ina he tango te ±. Tango 150\sqrt{18720169} mai i -1950.

$$x=\frac{-150\sqrt{18720169}-1950}{32500}$$

Whakawehe -1950-150\sqrt{18720169} ki te 32500.

$$x=-\frac{3\sqrt{18720169}}{650}-\frac{3}{50}$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{18720169}}{650}-\frac{3}{50} x=-\frac{3\sqrt{18720169}}{650}-\frac{3}{50}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 125x+15.

$$\left(125x^{2}+15x-50\times 40\right)\times 30+x\left(125x+15\right)\times 100=6420000$$

Whakareatia te 50 ki te 40, ka 2000.

$$\left(125x^{2}+15x-2000\right)\times 30+x\left(125x+15\right)\times 100=6420000$$

Whakamahia te āhuatanga tohatoha hei whakarea te 125x^{2}+15x-2000 ki te 30.

$$3750x^{2}+450x-60000+x\left(125x+15\right)\times 100=6420000$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 125x+15.

$$3750x^{2}+450x-60000+\left(125x^{2}+15x\right)\times 100=6420000$$

Whakamahia te āhuatanga tohatoha hei whakarea te 125x^{2}+15x ki te 100.

$$3750x^{2}+450x-60000+12500x^{2}+1500x=6420000$$

Pahekotia te 3750x^{2} me 12500x^{2}, ka 16250x^{2}.

$$16250x^{2}+450x-60000+1500x=6420000$$

Pahekotia te 450x me 1500x, ka 1950x.

$$16250x^{2}+1950x-60000=6420000$$

Me tāpiri te 60000 ki ngā taha e rua.

$$16250x^{2}+1950x=6420000+60000$$

Tāpirihia te 6420000 ki te 60000, ka 6480000.

$$16250x^{2}+1950x=6480000$$

Whakawehea ngā taha e rua ki te 16250.

$$\frac{16250x^{2}+1950x}{16250}=\frac{6480000}{16250}$$

Mā te whakawehe ki te 16250 ka wetekia te whakareanga ki te 16250.

$$x^{2}+\frac{1950}{16250}x=\frac{6480000}{16250}$$

Whakahekea te hautanga \frac{1950}{16250} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 650.

$$x^{2}+\frac{3}{25}x=\frac{6480000}{16250}$$

Whakahekea te hautanga \frac{6480000}{16250} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 1250.

$$x^{2}+\frac{3}{25}x=\frac{5184}{13}$$

Whakawehea te \frac{3}{25}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{50}. Nā, tāpiria te pūrua o te \frac{3}{50} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{3}{25}x+\left(\frac{3}{50}\right)^{2}=\frac{5184}{13}+\left(\frac{3}{50}\right)^{2}$$

Pūruatia \frac{3}{50} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{3}{25}x+\frac{9}{2500}=\frac{5184}{13}+\frac{9}{2500}$$

Tāpiri \frac{5184}{13} ki te \frac{9}{2500} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}+\frac{3}{25}x+\frac{9}{2500}=\frac{12960117}{32500}$$

Tauwehea x^{2}+\frac{3}{25}x+\frac{9}{2500}. 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}.

$$\left(x+\frac{3}{50}\right)^{2}=\frac{12960117}{32500}$$

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

$$\sqrt{\left(x+\frac{3}{50}\right)^{2}}=\sqrt{\frac{12960117}{32500}}$$

Whakarūnātia.

$$x+\frac{3}{50}=\frac{3\sqrt{18720169}}{650} x+\frac{3}{50}=-\frac{3\sqrt{18720169}}{650}$$

Me tango \frac{3}{50} mai i ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{18720169}}{650}-\frac{3}{50} x=-\frac{3\sqrt{18720169}}{650}-\frac{3}{50}$$