Whakaoti i te 2p^2+4p-5=0

$$2 p ^ { 2 } + 4 p - 5 = 0$$

Whakaoti mō p

$$p=\frac{\sqrt{14}}{2}-1\approx 0.870828693$$

$$p=-\frac{\sqrt{14}}{2}-1\approx -2.870828693$$

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.

$$2p^{2}+4p-5=0$$

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

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

Pūrua 4.

$$p=\frac{-4±\sqrt{16-4\times 2\left(-5\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$p=\frac{-4±\sqrt{16-8\left(-5\right)}}{2\times 2}$$

Whakareatia -8 ki te -5.

$$p=\frac{-4±\sqrt{16+40}}{2\times 2}$$

Tāpiri 16 ki te 40.

$$p=\frac{-4±\sqrt{56}}{2\times 2}$$

Tuhia te pūtakerua o te 56.

$$p=\frac{-4±2\sqrt{14}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$p=\frac{-4±2\sqrt{14}}{4}$$

Nā, me whakaoti te whārite p=\frac{-4±2\sqrt{14}}{4} ina he tāpiri te ±. Tāpiri -4 ki te 2\sqrt{14}.

$$p=\frac{2\sqrt{14}-4}{4}$$

Whakawehe -4+2\sqrt{14} ki te 4.

$$p=\frac{\sqrt{14}}{2}-1$$

Nā, me whakaoti te whārite p=\frac{-4±2\sqrt{14}}{4} ina he tango te ±. Tango 2\sqrt{14} mai i -4.

$$p=\frac{-2\sqrt{14}-4}{4}$$

Whakawehe -4-2\sqrt{14} ki te 4.

$$p=-\frac{\sqrt{14}}{2}-1$$

Kua oti te whārite te whakatau.

$$p=\frac{\sqrt{14}}{2}-1 p=-\frac{\sqrt{14}}{2}-1$$

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.

$$2p^{2}+4p-5=0$$

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

$$2p^{2}+4p-5-\left(-5\right)=-\left(-5\right)$$

Mā te tango i te -5 i a ia ake anō ka toe ko te 0.

$$2p^{2}+4p=-\left(-5\right)$$

Tango -5 mai i 0.

$$2p^{2}+4p=5$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2p^{2}+4p}{2}=\frac{5}{2}$$

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

$$p^{2}+\frac{4}{2}p=\frac{5}{2}$$

Whakawehe 4 ki te 2.

$$p^{2}+2p=\frac{5}{2}$$

Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$p^{2}+2p+1^{2}=\frac{5}{2}+1^{2}$$

Pūrua 1.

$$p^{2}+2p+1=\frac{5}{2}+1$$

Tāpiri \frac{5}{2} ki te 1.

$$p^{2}+2p+1=\frac{7}{2}$$

Tauwehea p^{2}+2p+1. 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}.

$$\left(p+1\right)^{2}=\frac{7}{2}$$

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

$$\sqrt{\left(p+1\right)^{2}}=\sqrt{\frac{7}{2}}$$

Whakarūnātia.

$$p+1=\frac{\sqrt{14}}{2} p+1=-\frac{\sqrt{14}}{2}$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$p=\frac{\sqrt{14}}{2}-1 p=-\frac{\sqrt{14}}{2}-1$$