a^2-6a-22=0 eching

$$a ^ { 2 } - 6 a - 22 = 0$$

a uchun yechish

$$a=\sqrt{31}+3\approx 8,567764363$$

$$a=3-\sqrt{31}\approx -2,567764363$$

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.

$$a^{2}-6a-22=0$$

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 -22 ni c bilan almashtiring.

$$a=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-22\right)}}{2}$$

-6 kvadratini chiqarish.

$$a=\frac{-\left(-6\right)±\sqrt{36-4\left(-22\right)}}{2}$$

-4 ni -22 marotabaga ko'paytirish.

$$a=\frac{-\left(-6\right)±\sqrt{36+88}}{2}$$

36 ni 88 ga qo'shish.

$$a=\frac{-\left(-6\right)±\sqrt{124}}{2}$$

124 ning kvadrat ildizini chiqarish.

$$a=\frac{-\left(-6\right)±2\sqrt{31}}{2}$$

-6 ning teskarisi 6 ga teng.

$$a=\frac{6±2\sqrt{31}}{2}$$

a=\frac{6±2\sqrt{31}}{2} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{31} ga qo'shish.

$$a=\frac{2\sqrt{31}+6}{2}$$

6+2\sqrt{31} ni 2 ga bo'lish.

$$a=\sqrt{31}+3$$

a=\frac{6±2\sqrt{31}}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{31} ni ayirish.

$$a=\frac{6-2\sqrt{31}}{2}$$

6-2\sqrt{31} ni 2 ga bo'lish.

$$a=3-\sqrt{31}$$

Tenglama yechildi.

$$a=\sqrt{31}+3 a=3-\sqrt{31}$$

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.

$$a^{2}-6a-22=0$$

22 ni tenglamaning ikkala tarafiga qo'shish.

$$a^{2}-6a-22-\left(-22\right)=-\left(-22\right)$$

O‘zidan -22 ayirilsa 0 qoladi.

$$a^{2}-6a=-\left(-22\right)$$

0 dan -22 ni ayirish.

$$a^{2}-6a=22$$

-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.

$$a^{2}-6a+\left(-3\right)^{2}=22+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$a^{2}-6a+9=22+9$$

22 ni 9 ga qo'shish.

$$a^{2}-6a+9=31$$

a^{2}-6a+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.

$$\left(a-3\right)^{2}=31$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a-3\right)^{2}}=\sqrt{31}$$

Qisqartirish.

$$a-3=\sqrt{31} a-3=-\sqrt{31}$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$a=\sqrt{31}+3 a=3-\sqrt{31}$$