x^2-6x-3=0 eching

$$x ^ { 2 } - 6 x - 3 = 0$$

x uchun yechish

$$x=2\sqrt{3}+3\approx 6,464101615$$

$$x=3-2\sqrt{3}\approx -0,464101615$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$x^{2}-6x-3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -6 ni b va -3 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-3\right)}}{2}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-3\right)}}{2}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+12}}{2}$$

36 ni 12 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{48}}{2}$$

48 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±4\sqrt{3}}{2}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±4\sqrt{3}}{2}$$

x=\frac{6±4\sqrt{3}}{2} tenglamasini yeching, bunda ± musbat. 6 ni 4\sqrt{3} ga qo'shish.

$$x=\frac{4\sqrt{3}+6}{2}$$

6+4\sqrt{3} ni 2 ga bo'lish.

$$x=2\sqrt{3}+3$$

x=\frac{6±4\sqrt{3}}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 4\sqrt{3} ni ayirish.

$$x=\frac{6-4\sqrt{3}}{2}$$

6-4\sqrt{3} ni 2 ga bo'lish.

$$x=3-2\sqrt{3}$$

Tenglama yechildi.

$$x=2\sqrt{3}+3 x=3-2\sqrt{3}$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}-6x-3=0$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-6x-3-\left(-3\right)=-\left(-3\right)$$

O‘zidan -3 ayirilsa 0 qoladi.

$$x^{2}-6x=-\left(-3\right)$$

0 dan -3 ni ayirish.

$$x^{2}-6x=3$$

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-6x+\left(-3\right)^{2}=3+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=3+9$$

3 ni 9 ga qo'shish.

$$x^{2}-6x+9=12$$

x^{2}-6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-3\right)^{2}=12$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-3=2\sqrt{3} x-3=-2\sqrt{3}$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2\sqrt{3}+3 x=3-2\sqrt{3}$$