Whakaoti i te 2*60*x+2*40*x+4x^2=2*2400

$$2 \times 60 \times x+2 \times 40 \times x+4 { x }^{ 2 } =2 \times 2400$$

Whakaoti mō x

$$x=5\sqrt{73}-25\approx 17.720018727$$

$$x=-5\sqrt{73}-25\approx -67.720018727$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Mahia ngā whakarea.

$$120x+80x+4x^{2}=2\times 2400$$

Pahekotia te 120x me 80x, ka 200x.

$$200x+4x^{2}=2\times 2400$$

Whakareatia te 2 ki te 2400, ka 4800.

$$200x+4x^{2}=4800$$

Tangohia te 4800 mai i ngā taha e rua.

$$200x+4x^{2}-4800=0$$

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.

$$4x^{2}+200x-4800=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 200 mō b, me -4800 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-200±\sqrt{200^{2}-4\times 4\left(-4800\right)}}{2\times 4}$$

Pūrua 200.

$$x=\frac{-200±\sqrt{40000-4\times 4\left(-4800\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-200±\sqrt{40000-16\left(-4800\right)}}{2\times 4}$$

Whakareatia -16 ki te -4800.

$$x=\frac{-200±\sqrt{40000+76800}}{2\times 4}$$

Tāpiri 40000 ki te 76800.

$$x=\frac{-200±\sqrt{116800}}{2\times 4}$$

Tuhia te pūtakerua o te 116800.

$$x=\frac{-200±40\sqrt{73}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-200±40\sqrt{73}}{8}$$

Nā, me whakaoti te whārite x=\frac{-200±40\sqrt{73}}{8} ina he tāpiri te ±. Tāpiri -200 ki te 40\sqrt{73}.

$$x=\frac{40\sqrt{73}-200}{8}$$

Whakawehe -200+40\sqrt{73} ki te 8.

$$x=5\sqrt{73}-25$$

Nā, me whakaoti te whārite x=\frac{-200±40\sqrt{73}}{8} ina he tango te ±. Tango 40\sqrt{73} mai i -200.

$$x=\frac{-40\sqrt{73}-200}{8}$$

Whakawehe -200-40\sqrt{73} ki te 8.

$$x=-5\sqrt{73}-25$$

Kua oti te whārite te whakatau.

$$x=5\sqrt{73}-25 x=-5\sqrt{73}-25$$

Ngā Upane mō te Whakaoti i te Pūrua

Mahia ngā whakarea.

$$120x+80x+4x^{2}=2\times 2400$$

Pahekotia te 120x me 80x, ka 200x.

$$200x+4x^{2}=2\times 2400$$

Whakareatia te 2 ki te 2400, ka 4800.

$$200x+4x^{2}=4800$$

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.

$$4x^{2}+200x=4800$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}+200x}{4}=\frac{4800}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$x^{2}+\frac{200}{4}x=\frac{4800}{4}$$

Whakawehe 200 ki te 4.

$$x^{2}+50x=\frac{4800}{4}$$

Whakawehe 4800 ki te 4.

$$x^{2}+50x=1200$$

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

$$x^{2}+50x+25^{2}=1200+25^{2}$$

Pūrua 25.

$$x^{2}+50x+625=1200+625$$

Tāpiri 1200 ki te 625.

$$x^{2}+50x+625=1825$$

Tauwehea x^{2}+50x+625. 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}.

$$\left(x+25\right)^{2}=1825$$

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

$$\sqrt{\left(x+25\right)^{2}}=\sqrt{1825}$$

Whakarūnātia.

$$x+25=5\sqrt{73} x+25=-5\sqrt{73}$$

Me tango 25 mai i ngā taha e rua o te whārite.

$$x=5\sqrt{73}-25 x=-5\sqrt{73}-25$$