Whakaoti i te x^2-45x-700=0

$${ x }^{ 2 } -45x-700=0$$

Whakaoti mō x

$$x = \frac{5 \sqrt{193} + 45}{2} \approx 57.231109974$$

$$x=\frac{45-5\sqrt{193}}{2}\approx -12.231109974$$

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.

$$x^{2}-45x-700=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -45 mō b, me -700 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-45\right)±\sqrt{\left(-45\right)^{2}-4\left(-700\right)}}{2}$$

Pūrua -45.

$$x=\frac{-\left(-45\right)±\sqrt{2025-4\left(-700\right)}}{2}$$

Whakareatia -4 ki te -700.

$$x=\frac{-\left(-45\right)±\sqrt{2025+2800}}{2}$$

Tāpiri 2025 ki te 2800.

$$x=\frac{-\left(-45\right)±\sqrt{4825}}{2}$$

Tuhia te pūtakerua o te 4825.

$$x=\frac{-\left(-45\right)±5\sqrt{193}}{2}$$

Ko te tauaro o -45 ko 45.

$$x=\frac{45±5\sqrt{193}}{2}$$

Nā, me whakaoti te whārite x=\frac{45±5\sqrt{193}}{2} ina he tāpiri te ±. Tāpiri 45 ki te 5\sqrt{193}.

$$x=\frac{5\sqrt{193}+45}{2}$$

Nā, me whakaoti te whārite x=\frac{45±5\sqrt{193}}{2} ina he tango te ±. Tango 5\sqrt{193} mai i 45.

$$x=\frac{45-5\sqrt{193}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{5\sqrt{193}+45}{2} x=\frac{45-5\sqrt{193}}{2}$$

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.

$$x^{2}-45x-700=0$$

Me tāpiri 700 ki ngā taha e rua o te whārite.

$$x^{2}-45x-700-\left(-700\right)=-\left(-700\right)$$

Mā te tango i te -700 i a ia ake anō ka toe ko te 0.

$$x^{2}-45x=-\left(-700\right)$$

Tango -700 mai i 0.

$$x^{2}-45x=700$$

Whakawehea te -45, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{45}{2}. Nā, tāpiria te pūrua o te -\frac{45}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-45x+\left(-\frac{45}{2}\right)^{2}=700+\left(-\frac{45}{2}\right)^{2}$$

Pūruatia -\frac{45}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-45x+\frac{2025}{4}=700+\frac{2025}{4}$$

Tāpiri 700 ki te \frac{2025}{4}.

$$x^{2}-45x+\frac{2025}{4}=\frac{4825}{4}$$

Tauwehea x^{2}-45x+\frac{2025}{4}. 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}.

$$\left(x-\frac{45}{2}\right)^{2}=\frac{4825}{4}$$

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

$$\sqrt{\left(x-\frac{45}{2}\right)^{2}}=\sqrt{\frac{4825}{4}}$$

Whakarūnātia.

$$x-\frac{45}{2}=\frac{5\sqrt{193}}{2} x-\frac{45}{2}=-\frac{5\sqrt{193}}{2}$$

Me tāpiri \frac{45}{2} ki ngā taha e rua o te whārite.

$$x=\frac{5\sqrt{193}+45}{2} x=\frac{45-5\sqrt{193}}{2}$$