Whakaoti i te x^2-20=55x

$${ x }^{ 2 } -20 = 55x$$

Whakaoti mō x

$$x = \frac{3 \sqrt{345} + 55}{2} \approx 55.361263432$$

$$x=\frac{55-3\sqrt{345}}{2}\approx -0.361263432$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 55x mai i ngā taha e rua.

$$x^{2}-20-55x=0$$

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.

$$x^{2}-55x-20=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -55 mō b, me -20 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-55\right)±\sqrt{\left(-55\right)^{2}-4\left(-20\right)}}{2}$$

Pūrua -55.

$$x=\frac{-\left(-55\right)±\sqrt{3025-4\left(-20\right)}}{2}$$

Whakareatia -4 ki te -20.

$$x=\frac{-\left(-55\right)±\sqrt{3025+80}}{2}$$

Tāpiri 3025 ki te 80.

$$x=\frac{-\left(-55\right)±\sqrt{3105}}{2}$$

Tuhia te pūtakerua o te 3105.

$$x=\frac{-\left(-55\right)±3\sqrt{345}}{2}$$

Ko te tauaro o -55 ko 55.

$$x=\frac{55±3\sqrt{345}}{2}$$

Nā, me whakaoti te whārite x=\frac{55±3\sqrt{345}}{2} ina he tāpiri te ±. Tāpiri 55 ki te 3\sqrt{345}.

$$x=\frac{3\sqrt{345}+55}{2}$$

Nā, me whakaoti te whārite x=\frac{55±3\sqrt{345}}{2} ina he tango te ±. Tango 3\sqrt{345} mai i 55.

$$x=\frac{55-3\sqrt{345}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{345}+55}{2} x=\frac{55-3\sqrt{345}}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 55x mai i ngā taha e rua.

$$x^{2}-20-55x=0$$

Me tāpiri te 20 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}-55x=20$$

Whakawehea te -55, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{55}{2}. Nā, tāpiria te pūrua o te -\frac{55}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-55x+\left(-\frac{55}{2}\right)^{2}=20+\left(-\frac{55}{2}\right)^{2}$$

Pūruatia -\frac{55}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-55x+\frac{3025}{4}=20+\frac{3025}{4}$$

Tāpiri 20 ki te \frac{3025}{4}.

$$x^{2}-55x+\frac{3025}{4}=\frac{3105}{4}$$

Tauwehea x^{2}-55x+\frac{3025}{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}.

$$\left(x-\frac{55}{2}\right)^{2}=\frac{3105}{4}$$

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

$$\sqrt{\left(x-\frac{55}{2}\right)^{2}}=\sqrt{\frac{3105}{4}}$$

Whakarūnātia.

$$x-\frac{55}{2}=\frac{3\sqrt{345}}{2} x-\frac{55}{2}=-\frac{3\sqrt{345}}{2}$$

Me tāpiri \frac{55}{2} ki ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{345}+55}{2} x=\frac{55-3\sqrt{345}}{2}$$