a^2-4a-46=0 eching

$$a ^ { 2 } - 4 a - 46 = 0$$

a uchun yechish

$$a=5\sqrt{2}+2\approx 9,071067812$$

$$a=2-5\sqrt{2}\approx -5,071067812$$

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.

$$a^{2}-4a-46=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -4 ni b va -46 ni c bilan almashtiring.

$$a=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-46\right)}}{2}$$

-4 kvadratini chiqarish.

$$a=\frac{-\left(-4\right)±\sqrt{16-4\left(-46\right)}}{2}$$

-4 ni -46 marotabaga ko'paytirish.

$$a=\frac{-\left(-4\right)±\sqrt{16+184}}{2}$$

16 ni 184 ga qo'shish.

$$a=\frac{-\left(-4\right)±\sqrt{200}}{2}$$

200 ning kvadrat ildizini chiqarish.

$$a=\frac{-\left(-4\right)±10\sqrt{2}}{2}$$

-4 ning teskarisi 4 ga teng.

$$a=\frac{4±10\sqrt{2}}{2}$$

a=\frac{4±10\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. 4 ni 10\sqrt{2} ga qo'shish.

$$a=\frac{10\sqrt{2}+4}{2}$$

4+10\sqrt{2} ni 2 ga bo'lish.

$$a=5\sqrt{2}+2$$

a=\frac{4±10\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 10\sqrt{2} ni ayirish.

$$a=\frac{4-10\sqrt{2}}{2}$$

4-10\sqrt{2} ni 2 ga bo'lish.

$$a=2-5\sqrt{2}$$

Tenglama yechildi.

$$a=5\sqrt{2}+2 a=2-5\sqrt{2}$$

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.

$$a^{2}-4a-46=0$$

46 ni tenglamaning ikkala tarafiga qo'shish.

$$a^{2}-4a-46-\left(-46\right)=-\left(-46\right)$$

O‘zidan -46 ayirilsa 0 qoladi.

$$a^{2}-4a=-\left(-46\right)$$

0 dan -46 ni ayirish.

$$a^{2}-4a=46$$

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

$$a^{2}-4a+\left(-2\right)^{2}=46+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$a^{2}-4a+4=46+4$$

46 ni 4 ga qo'shish.

$$a^{2}-4a+4=50$$

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

$$\left(a-2\right)^{2}=50$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a-2\right)^{2}}=\sqrt{50}$$

Qisqartirish.

$$a-2=5\sqrt{2} a-2=-5\sqrt{2}$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$a=5\sqrt{2}+2 a=2-5\sqrt{2}$$