Whakaoti i te pix^2+3x+01415926=0

$$\pi { x }^{ 2 } +3x+01415926=0$$

Whakaoti mō x

$$x=-\frac{3}{\pi }\approx -0.954929659$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakareatia te 0 ki te 1415926, ka 0.

$$\pi x^{2}+3x+0=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$\pi x^{2}+3x=0$$

Tauwehea te x.

$$x\left(\pi x+3\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te \pi x+3=0.

$$x=0 x=-\frac{3}{\pi }$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 1415926, ka 0.

$$\pi x^{2}+3x+0=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$\pi x^{2}+3x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \pi mō a, 3 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}}}{2\pi }$$

Tuhia te pūtakerua o te 3^{2}.

$$x=\frac{-3±3}{2\pi }$$

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

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

Whakawehe 0 ki te 2\pi .

$$x=0$$

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

$$x=-\frac{6}{2\pi }$$

Whakawehe -6 ki te 2\pi .

$$x=-\frac{3}{\pi }$$

Kua oti te whārite te whakatau.

$$x=0 x=-\frac{3}{\pi }$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 0 ki te 1415926, ka 0.

$$\pi x^{2}+3x+0=0$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$\pi x^{2}+3x=0$$

Whakawehea ngā taha e rua ki te \pi .

$$\frac{\pi x^{2}+3x}{\pi }=\frac{0}{\pi }$$

Mā te whakawehe ki te \pi ka wetekia te whakareanga ki te \pi .

$$x^{2}+\frac{3}{\pi }x=\frac{0}{\pi }$$

Whakawehe 0 ki te \pi .

$$x^{2}+\frac{3}{\pi }x=0$$

Whakawehea te \frac{3}{\pi }, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{2\pi }. Nā, tāpiria te pūrua o te \frac{3}{2\pi } ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{3}{\pi }x+\left(\frac{3}{2\pi }\right)^{2}=\left(\frac{3}{2\pi }\right)^{2}$$

Pūrua \frac{3}{2\pi }.

$$x^{2}+\frac{3}{\pi }x+\frac{9}{4\pi ^{2}}=\frac{9}{4\pi ^{2}}$$

Tauwehea te x^{2}+\frac{3}{\pi }x+\frac{9}{4\pi ^{2}}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{3}{2\pi }\right)^{2}=\frac{9}{4\pi ^{2}}$$

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

$$\sqrt{\left(x+\frac{3}{2\pi }\right)^{2}}=\sqrt{\frac{9}{4\pi ^{2}}}$$

Whakarūnātia.

$$x+\frac{3}{2\pi }=\frac{3}{2\pi } x+\frac{3}{2\pi }=-\frac{3}{2\pi }$$

Me tango \frac{3}{2\pi } mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{3}{\pi }$$