Whakaoti i te x^2-40x-800=0

$$x ^ { 2 } - 40 x - 800 = 0$$

Whakaoti mō x

$$x=20\sqrt{3}+20\approx 54.641016151$$

$$x=20-20\sqrt{3}\approx -14.641016151$$

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.

$$x^{2}-40x-800=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -40 mō b, me -800 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-40\right)±\sqrt{\left(-40\right)^{2}-4\left(-800\right)}}{2}$$

Pūrua -40.

$$x=\frac{-\left(-40\right)±\sqrt{1600-4\left(-800\right)}}{2}$$

Whakareatia -4 ki te -800.

$$x=\frac{-\left(-40\right)±\sqrt{1600+3200}}{2}$$

Tāpiri 1600 ki te 3200.

$$x=\frac{-\left(-40\right)±\sqrt{4800}}{2}$$

Tuhia te pūtakerua o te 4800.

$$x=\frac{-\left(-40\right)±40\sqrt{3}}{2}$$

Ko te tauaro o -40 ko 40.

$$x=\frac{40±40\sqrt{3}}{2}$$

Nā, me whakaoti te whārite x=\frac{40±40\sqrt{3}}{2} ina he tāpiri te ±. Tāpiri 40 ki te 40\sqrt{3}.

$$x=\frac{40\sqrt{3}+40}{2}$$

Whakawehe 40+40\sqrt{3} ki te 2.

$$x=20\sqrt{3}+20$$

Nā, me whakaoti te whārite x=\frac{40±40\sqrt{3}}{2} ina he tango te ±. Tango 40\sqrt{3} mai i 40.

$$x=\frac{40-40\sqrt{3}}{2}$$

Whakawehe 40-40\sqrt{3} ki te 2.

$$x=20-20\sqrt{3}$$

Kua oti te whārite te whakatau.

$$x=20\sqrt{3}+20 x=20-20\sqrt{3}$$

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.

$$x^{2}-40x-800=0$$

Me tāpiri 800 ki ngā taha e rua o te whārite.

$$x^{2}-40x-800-\left(-800\right)=-\left(-800\right)$$

Mā te tango i te -800 i a ia ake anō ka toe ko te 0.

$$x^{2}-40x=-\left(-800\right)$$

Tango -800 mai i 0.

$$x^{2}-40x=800$$

Whakawehea te -40, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -20. Nā, tāpiria te pūrua o te -20 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-40x+\left(-20\right)^{2}=800+\left(-20\right)^{2}$$

Pūrua -20.

$$x^{2}-40x+400=800+400$$

Tāpiri 800 ki te 400.

$$x^{2}-40x+400=1200$$

Tauwehea x^{2}-40x+400. 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}.

$$\left(x-20\right)^{2}=1200$$

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

$$\sqrt{\left(x-20\right)^{2}}=\sqrt{1200}$$

Whakarūnātia.

$$x-20=20\sqrt{3} x-20=-20\sqrt{3}$$

Me tāpiri 20 ki ngā taha e rua o te whārite.

$$x=20\sqrt{3}+20 x=20-20\sqrt{3}$$