Whakaoti i te (2x-40)(3x-50)*(30+100)+2000*1000=64000

$$( 2 x - 40 ) ( 3 x - 50 ) \times ( 30 + 100 ) + 2000 \times 1000 = 64000$$

Whakaoti mō x (complex solution)

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3}\approx 18.333333333+49.792303665i$$

$$x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}\approx 18.333333333-49.792303665i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 30 ki te 100, ka 130.

$$\left(2x-40\right)\left(3x-50\right)\times 130+2000\times 1000=64000$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-40 ki te 3x-50 ka whakakotahi i ngā kupu rite.

$$\left(6x^{2}-220x+2000\right)\times 130+2000\times 1000=64000$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}-220x+2000 ki te 130.

$$780x^{2}-28600x+260000+2000\times 1000=64000$$

Whakareatia te 2000 ki te 1000, ka 2000000.

$$780x^{2}-28600x+260000+2000000=64000$$

Tāpirihia te 260000 ki te 2000000, ka 2260000.

$$780x^{2}-28600x+2260000=64000$$

Tangohia te 64000 mai i ngā taha e rua.

$$780x^{2}-28600x+2260000-64000=0$$

Tangohia te 64000 i te 2260000, ka 2196000.

$$780x^{2}-28600x+2196000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 780 mō a, -28600 mō b, me 2196000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-28600\right)±\sqrt{\left(-28600\right)^{2}-4\times 780\times 2196000}}{2\times 780}$$

Pūrua -28600.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-4\times 780\times 2196000}}{2\times 780}$$

Whakareatia -4 ki te 780.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-3120\times 2196000}}{2\times 780}$$

Whakareatia -3120 ki te 2196000.

$$x=\frac{-\left(-28600\right)±\sqrt{817960000-6851520000}}{2\times 780}$$

Tāpiri 817960000 ki te -6851520000.

$$x=\frac{-\left(-28600\right)±\sqrt{-6033560000}}{2\times 780}$$

Tuhia te pūtakerua o te -6033560000.

$$x=\frac{-\left(-28600\right)±200\sqrt{150839}i}{2\times 780}$$

Ko te tauaro o -28600 ko 28600.

$$x=\frac{28600±200\sqrt{150839}i}{2\times 780}$$

Whakareatia 2 ki te 780.

$$x=\frac{28600±200\sqrt{150839}i}{1560}$$

Nā, me whakaoti te whārite x=\frac{28600±200\sqrt{150839}i}{1560} ina he tāpiri te ±. Tāpiri 28600 ki te 200i\sqrt{150839}.

$$x=\frac{28600+200\sqrt{150839}i}{1560}$$

Whakawehe 28600+200i\sqrt{150839} ki te 1560.

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$

Nā, me whakaoti te whārite x=\frac{28600±200\sqrt{150839}i}{1560} ina he tango te ±. Tango 200i\sqrt{150839} mai i 28600.

$$x=\frac{-200\sqrt{150839}i+28600}{1560}$$

Whakawehe 28600-200i\sqrt{150839} ki te 1560.

$$x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3} x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tāpirihia te 30 ki te 100, ka 130.

$$\left(2x-40\right)\left(3x-50\right)\times 130+2000\times 1000=64000$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-40 ki te 3x-50 ka whakakotahi i ngā kupu rite.

$$\left(6x^{2}-220x+2000\right)\times 130+2000\times 1000=64000$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6x^{2}-220x+2000 ki te 130.

$$780x^{2}-28600x+260000+2000\times 1000=64000$$

Whakareatia te 2000 ki te 1000, ka 2000000.

$$780x^{2}-28600x+260000+2000000=64000$$

Tāpirihia te 260000 ki te 2000000, ka 2260000.

$$780x^{2}-28600x+2260000=64000$$

Tangohia te 2260000 mai i ngā taha e rua.

$$780x^{2}-28600x=64000-2260000$$

Tangohia te 2260000 i te 64000, ka -2196000.

$$780x^{2}-28600x=-2196000$$

Whakawehea ngā taha e rua ki te 780.

$$\frac{780x^{2}-28600x}{780}=-\frac{2196000}{780}$$

Mā te whakawehe ki te 780 ka wetekia te whakareanga ki te 780.

$$x^{2}+\left(-\frac{28600}{780}\right)x=-\frac{2196000}{780}$$

Whakahekea te hautanga \frac{-28600}{780} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 260.

$$x^{2}-\frac{110}{3}x=-\frac{2196000}{780}$$

Whakahekea te hautanga \frac{-2196000}{780} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 60.

$$x^{2}-\frac{110}{3}x=-\frac{36600}{13}$$

Whakawehea te -\frac{110}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{55}{3}. Nā, tāpiria te pūrua o te -\frac{55}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{110}{3}x+\left(-\frac{55}{3}\right)^{2}=-\frac{36600}{13}+\left(-\frac{55}{3}\right)^{2}$$

Pūruatia -\frac{55}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{110}{3}x+\frac{3025}{9}=-\frac{36600}{13}+\frac{3025}{9}$$

Tāpiri -\frac{36600}{13} ki te \frac{3025}{9} 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.

$$x^{2}-\frac{110}{3}x+\frac{3025}{9}=-\frac{290075}{117}$$

Tauwehea x^{2}-\frac{110}{3}x+\frac{3025}{9}. 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}.

$$\left(x-\frac{55}{3}\right)^{2}=-\frac{290075}{117}$$

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

$$\sqrt{\left(x-\frac{55}{3}\right)^{2}}=\sqrt{-\frac{290075}{117}}$$

Whakarūnātia.

$$x-\frac{55}{3}=\frac{5\sqrt{150839}i}{39} x-\frac{55}{3}=-\frac{5\sqrt{150839}i}{39}$$

Me tāpiri \frac{55}{3} ki ngā taha e rua o te whārite.

$$x=\frac{5\sqrt{150839}i}{39}+\frac{55}{3} x=-\frac{5\sqrt{150839}i}{39}+\frac{55}{3}$$