a^2-2a-30=0 eching

$$a ^ { 2 } - 2 a - 30 = 0$$

a uchun yechish

$$a=\sqrt{31}+1\approx 6,567764363$$

$$a=1-\sqrt{31}\approx -4,567764363$$

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.

$$a^{2}-2a-30=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -2 ni b va -30 ni c bilan almashtiring.

$$a=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-30\right)}}{2}$$

-2 kvadratini chiqarish.

$$a=\frac{-\left(-2\right)±\sqrt{4-4\left(-30\right)}}{2}$$

-4 ni -30 marotabaga ko'paytirish.

$$a=\frac{-\left(-2\right)±\sqrt{4+120}}{2}$$

4 ni 120 ga qo'shish.

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

124 ning kvadrat ildizini chiqarish.

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

-2 ning teskarisi 2 ga teng.

$$a=\frac{2±2\sqrt{31}}{2}$$

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

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

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

$$a=\sqrt{31}+1$$

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

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

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

$$a=1-\sqrt{31}$$

Tenglama yechildi.

$$a=\sqrt{31}+1 a=1-\sqrt{31}$$

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.

$$a^{2}-2a-30=0$$

30 ni tenglamaning ikkala tarafiga qo'shish.

$$a^{2}-2a-30-\left(-30\right)=-\left(-30\right)$$

O‘zidan -30 ayirilsa 0 qoladi.

$$a^{2}-2a=-\left(-30\right)$$

0 dan -30 ni ayirish.

$$a^{2}-2a=30$$

-2 ni bo‘lish, x shartining koeffitsienti, 2 ga -1 olish uchun. Keyin, -1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}-2a+1=30+1$$

30 ni 1 ga qo'shish.

$$a^{2}-2a+1=31$$

a^{2}-2a+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(a-1\right)^{2}=31$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a-1\right)^{2}}=\sqrt{31}$$

Qisqartirish.

$$a-1=\sqrt{31} a-1=-\sqrt{31}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$a=\sqrt{31}+1 a=1-\sqrt{31}$$