Whakaoti i te x^2-5x=0:pi

$$x ^ { 2 } - 5 x = 0 : \pi$$

Whakaoti mō x

$$x=5$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te \frac{0}{\pi } mai i ngā taha e rua.

$$x^{2}-5x-\frac{0}{\pi }=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x^{2}-5x ki te \frac{\pi }{\pi }.

$$\frac{\left(x^{2}-5x\right)\pi }{\pi }-\frac{0}{\pi }=0$$

Tā te mea he rite te tauraro o \frac{\left(x^{2}-5x\right)\pi }{\pi } me \frac{0}{\pi }, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\left(x^{2}-5x\right)\pi -0}{\pi }=0$$

Mahia ngā whakarea i roto o \left(x^{2}-5x\right)\pi -0.

$$\frac{x^{2}\pi -5x\pi }{\pi }=0$$

Whakawehea ia wā o x^{2}\pi -5x\pi ki te \pi , kia riro ko -5x+x^{2}.

$$-5x+x^{2}=0$$

Tauwehea te x.

$$x\left(-5+x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -5+x=0.

$$x=0 x=5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te \frac{0}{\pi } mai i ngā taha e rua.

$$x^{2}-5x-\frac{0}{\pi }=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x^{2}-5x ki te \frac{\pi }{\pi }.

$$\frac{\left(x^{2}-5x\right)\pi }{\pi }-\frac{0}{\pi }=0$$

Tā te mea he rite te tauraro o \frac{\left(x^{2}-5x\right)\pi }{\pi } me \frac{0}{\pi }, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\left(x^{2}-5x\right)\pi -0}{\pi }=0$$

Mahia ngā whakarea i roto o \left(x^{2}-5x\right)\pi -0.

$$\frac{x^{2}\pi -5x\pi }{\pi }=0$$

Whakawehea ia wā o x^{2}\pi -5x\pi ki te \pi , kia riro ko -5x+x^{2}.

$$-5x+x^{2}=0$$

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.

$$x^{2}-5x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -5 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Tuhia te pūtakerua o te \left(-5\right)^{2}.

$$x=\frac{-\left(-5\right)±5}{2}$$

Ko te tauaro o -5 ko 5.

$$x=\frac{5±5}{2}$$

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

$$x=\frac{10}{2}$$

Whakawehe 10 ki te 2.

$$x=5$$

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

$$x=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=5 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te \frac{0}{\pi } mai i ngā taha e rua.

$$x^{2}-5x-\frac{0}{\pi }=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x^{2}-5x ki te \frac{\pi }{\pi }.

$$\frac{\left(x^{2}-5x\right)\pi }{\pi }-\frac{0}{\pi }=0$$

Tā te mea he rite te tauraro o \frac{\left(x^{2}-5x\right)\pi }{\pi } me \frac{0}{\pi }, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\left(x^{2}-5x\right)\pi -0}{\pi }=0$$

Mahia ngā whakarea i roto o \left(x^{2}-5x\right)\pi -0.

$$\frac{x^{2}\pi -5x\pi }{\pi }=0$$

Whakawehea ia wā o x^{2}\pi -5x\pi ki te \pi , kia riro ko -5x+x^{2}.

$$-5x+x^{2}=0$$

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.

$$x^{2}-5x=0$$

Whakawehea te -5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{2}. Nā, tāpiria te pūrua o te -\frac{5}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-5x+\left(-\frac{5}{2}\right)^{2}=\left(-\frac{5}{2}\right)^{2}$$

Pūruatia -\frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-5x+\frac{25}{4}=\frac{25}{4}$$

Tauwehea x^{2}-5x+\frac{25}{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}.

$$\left(x-\frac{5}{2}\right)^{2}=\frac{25}{4}$$

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

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Whakarūnātia.

$$x-\frac{5}{2}=\frac{5}{2} x-\frac{5}{2}=-\frac{5}{2}$$

Me tāpiri \frac{5}{2} ki ngā taha e rua o te whārite.

$$x=5 x=0$$