4x^2=12-3x eching

$$4 x ^ { 2 } = 12 - 3 x$$

x uchun yechish

$$x = \frac{\sqrt{201} - 3}{8} \approx 1,39718086$$

$$x=\frac{-\sqrt{201}-3}{8}\approx -2,14718086$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 12 ni ayirish.

$$4x^{2}-12=-3x$$

3x ni ikki tarafga qo’shing.

$$4x^{2}-12+3x=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$4x^{2}+3x-12=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 3 ni b va -12 ni c bilan almashtiring.

$$x=\frac{-3±\sqrt{3^{2}-4\times 4\left(-12\right)}}{2\times 4}$$

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\times 4\left(-12\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9-16\left(-12\right)}}{2\times 4}$$

-16 ni -12 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+192}}{2\times 4}$$

9 ni 192 ga qo'shish.

$$x=\frac{-3±\sqrt{201}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{201}}{8}$$

x=\frac{-3±\sqrt{201}}{8} tenglamasini yeching, bunda ± musbat. -3 ni \sqrt{201} ga qo'shish.

$$x=\frac{\sqrt{201}-3}{8}$$

x=\frac{-3±\sqrt{201}}{8} tenglamasini yeching, bunda ± manfiy. -3 dan \sqrt{201} ni ayirish.

$$x=\frac{-\sqrt{201}-3}{8}$$

Tenglama yechildi.

$$x=\frac{\sqrt{201}-3}{8} x=\frac{-\sqrt{201}-3}{8}$$

Kvadratni yakunlash bo'yicha qadamlar

3x ni ikki tarafga qo’shing.

$$4x^{2}+3x=12$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}+3x}{4}=\frac{12}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{3}{4}x=\frac{12}{4}$$

12 ni 4 ga bo'lish.

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

\frac{3}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{8} olish uchun. Keyin, \frac{3}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{3}{4}x+\left(\frac{3}{8}\right)^{2}=3+\left(\frac{3}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{8} kvadratini chiqarish.

$$x^{2}+\frac{3}{4}x+\frac{9}{64}=3+\frac{9}{64}$$

3 ni \frac{9}{64} ga qo'shish.

$$x^{2}+\frac{3}{4}x+\frac{9}{64}=\frac{201}{64}$$

x^{2}+\frac{3}{4}x+\frac{9}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{3}{8}\right)^{2}=\frac{201}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{8}\right)^{2}}=\sqrt{\frac{201}{64}}$$

Qisqartirish.

$$x+\frac{3}{8}=\frac{\sqrt{201}}{8} x+\frac{3}{8}=-\frac{\sqrt{201}}{8}$$

Tenglamaning ikkala tarafidan \frac{3}{8} ni ayirish.

$$x=\frac{\sqrt{201}-3}{8} x=\frac{-\sqrt{201}-3}{8}$$