Whakaoti i te 5x^2-43x-125=7x

$$5 { x }^{ 2 } -43x-125=7x$$

Whakaoti mō x

$$x=5\sqrt{2}+5\approx 12.071067812$$

$$x=5-5\sqrt{2}\approx -2.071067812$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 7x mai i ngā taha e rua.

$$5x^{2}-43x-125-7x=0$$

Pahekotia te -43x me -7x, ka -50x.

$$5x^{2}-50x-125=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -50 mō b, me -125 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-50\right)±\sqrt{\left(-50\right)^{2}-4\times 5\left(-125\right)}}{2\times 5}$$

Pūrua -50.

$$x=\frac{-\left(-50\right)±\sqrt{2500-4\times 5\left(-125\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-50\right)±\sqrt{2500-20\left(-125\right)}}{2\times 5}$$

Whakareatia -20 ki te -125.

$$x=\frac{-\left(-50\right)±\sqrt{2500+2500}}{2\times 5}$$

Tāpiri 2500 ki te 2500.

$$x=\frac{-\left(-50\right)±\sqrt{5000}}{2\times 5}$$

Tuhia te pūtakerua o te 5000.

$$x=\frac{-\left(-50\right)±50\sqrt{2}}{2\times 5}$$

Ko te tauaro o -50 ko 50.

$$x=\frac{50±50\sqrt{2}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{50±50\sqrt{2}}{10}$$

Nā, me whakaoti te whārite x=\frac{50±50\sqrt{2}}{10} ina he tāpiri te ±. Tāpiri 50 ki te 50\sqrt{2}.

$$x=\frac{50\sqrt{2}+50}{10}$$

Whakawehe 50+50\sqrt{2} ki te 10.

$$x=5\sqrt{2}+5$$

Nā, me whakaoti te whārite x=\frac{50±50\sqrt{2}}{10} ina he tango te ±. Tango 50\sqrt{2} mai i 50.

$$x=\frac{50-50\sqrt{2}}{10}$$

Whakawehe 50-50\sqrt{2} ki te 10.

$$x=5-5\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=5\sqrt{2}+5 x=5-5\sqrt{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 7x mai i ngā taha e rua.

$$5x^{2}-43x-125-7x=0$$

Pahekotia te -43x me -7x, ka -50x.

$$5x^{2}-50x-125=0$$

Me tāpiri te 125 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$5x^{2}-50x=125$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}-50x}{5}=\frac{125}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$x^{2}+\left(-\frac{50}{5}\right)x=\frac{125}{5}$$

Whakawehe -50 ki te 5.

$$x^{2}-10x=\frac{125}{5}$$

Whakawehe 125 ki te 5.

$$x^{2}-10x=25$$

Whakawehea te -10, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -5. Nā, tāpiria te pūrua o te -5 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-10x+\left(-5\right)^{2}=25+\left(-5\right)^{2}$$

Pūrua -5.

$$x^{2}-10x+25=25+25$$

Tāpiri 25 ki te 25.

$$x^{2}-10x+25=50$$

Tauwehea te x^{2}-10x+25. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-5\right)^{2}=50$$

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

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{50}$$

Whakarūnātia.

$$x-5=5\sqrt{2} x-5=-5\sqrt{2}$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$x=5\sqrt{2}+5 x=5-5\sqrt{2}$$