pix^2+3x+01415926=0 eching

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

x uchun yechish

$$x=-\frac{3}{\pi }\approx -0,954929659$$

$$x=0$$

Faktorlash qadamlari

0 hosil qilish uchun 0 va 1415926 ni ko'paytirish.

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

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

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

x omili.

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

Tenglamani yechish uchun x=0 va \pi x+3=0 ni yeching.

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

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 1415926 ni ko'paytirish.

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

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \pi ni a, 3 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-3±\sqrt{3^{2}}}{2\pi }$$

3^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-3±3}{2\pi }$$

x=\frac{-3±3}{2\pi } tenglamasini yeching, bunda ± musbat. -3 ni 3 ga qo'shish.

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

0 ni 2\pi ga bo'lish.

$$x=0$$

x=\frac{-3±3}{2\pi } tenglamasini yeching, bunda ± manfiy. -3 dan 3 ni ayirish.

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

-6 ni 2\pi ga bo'lish.

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 1415926 ni ko'paytirish.

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

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

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

Ikki tarafini \pi ga bo‘ling.

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

\pi ga bo'lish \pi ga ko'paytirishni bekor qiladi.

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

0 ni \pi ga bo'lish.

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

\frac{3}{\pi } ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{2\pi } olish uchun. Keyin, \frac{3}{2\pi } ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

\frac{3}{2\pi } kvadratini chiqarish.

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

x^{2}+\frac{3}{\pi }x+\frac{9}{4\pi ^{2}} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

Tenglamaning ikkala tarafidan \frac{3}{2\pi } ni ayirish.

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