Whakaoti i te 2x^2-7500+300x=0

$$2 { x }^{ 2 } -7500+300x=0$$

Whakaoti mō x

$$x=25\sqrt{15}-75\approx 21.824583655$$

$$x=-25\sqrt{15}-75\approx -171.824583655$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$2x^{2}+300x-7500=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 300 mō b, me -7500 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-300±\sqrt{300^{2}-4\times 2\left(-7500\right)}}{2\times 2}$$

Pūrua 300.

$$x=\frac{-300±\sqrt{90000-4\times 2\left(-7500\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-300±\sqrt{90000-8\left(-7500\right)}}{2\times 2}$$

Whakareatia -8 ki te -7500.

$$x=\frac{-300±\sqrt{90000+60000}}{2\times 2}$$

Tāpiri 90000 ki te 60000.

$$x=\frac{-300±\sqrt{150000}}{2\times 2}$$

Tuhia te pūtakerua o te 150000.

$$x=\frac{-300±100\sqrt{15}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-300±100\sqrt{15}}{4}$$

Nā, me whakaoti te whārite x=\frac{-300±100\sqrt{15}}{4} ina he tāpiri te ±. Tāpiri -300 ki te 100\sqrt{15}.

$$x=\frac{100\sqrt{15}-300}{4}$$

Whakawehe -300+100\sqrt{15} ki te 4.

$$x=25\sqrt{15}-75$$

Nā, me whakaoti te whārite x=\frac{-300±100\sqrt{15}}{4} ina he tango te ±. Tango 100\sqrt{15} mai i -300.

$$x=\frac{-100\sqrt{15}-300}{4}$$

Whakawehe -300-100\sqrt{15} ki te 4.

$$x=-25\sqrt{15}-75$$

Kua oti te whārite te whakatau.

$$x=25\sqrt{15}-75 x=-25\sqrt{15}-75$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$2x^{2}+300x-7500=0$$

Me tāpiri 7500 ki ngā taha e rua o te whārite.

$$2x^{2}+300x-7500-\left(-7500\right)=-\left(-7500\right)$$

Mā te tango i te -7500 i a ia ake anō ka toe ko te 0.

$$2x^{2}+300x=-\left(-7500\right)$$

Tango -7500 mai i 0.

$$2x^{2}+300x=7500$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+300x}{2}=\frac{7500}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\frac{300}{2}x=\frac{7500}{2}$$

Whakawehe 300 ki te 2.

$$x^{2}+150x=\frac{7500}{2}$$

Whakawehe 7500 ki te 2.

$$x^{2}+150x=3750$$

Whakawehea te 150, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 75. Nā, tāpiria te pūrua o te 75 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+150x+75^{2}=3750+75^{2}$$

Pūrua 75.

$$x^{2}+150x+5625=3750+5625$$

Tāpiri 3750 ki te 5625.

$$x^{2}+150x+5625=9375$$

Tauwehea x^{2}+150x+5625. 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}.

$$\left(x+75\right)^{2}=9375$$

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

$$\sqrt{\left(x+75\right)^{2}}=\sqrt{9375}$$

Whakarūnātia.

$$x+75=25\sqrt{15} x+75=-25\sqrt{15}$$

Me tango 75 mai i ngā taha e rua o te whārite.

$$x=25\sqrt{15}-75 x=-25\sqrt{15}-75$$