x^2-20x-192=0 eching

$$x ^ { 2 } - 20 x - 192 = 0$$

x uchun yechish

$$x=2\sqrt{73}+10\approx 27,088007491$$

$$x=10-2\sqrt{73}\approx -7,088007491$$

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.

$$x^{2}-20x-192=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -20 ni b va -192 ni c bilan almashtiring.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\left(-192\right)}}{2}$$

-20 kvadratini chiqarish.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\left(-192\right)}}{2}$$

-4 ni -192 marotabaga ko'paytirish.

$$x=\frac{-\left(-20\right)±\sqrt{400+768}}{2}$$

400 ni 768 ga qo'shish.

$$x=\frac{-\left(-20\right)±\sqrt{1168}}{2}$$

1168 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-20\right)±4\sqrt{73}}{2}$$

-20 ning teskarisi 20 ga teng.

$$x=\frac{20±4\sqrt{73}}{2}$$

x=\frac{20±4\sqrt{73}}{2} tenglamasini yeching, bunda ± musbat. 20 ni 4\sqrt{73} ga qo'shish.

$$x=\frac{4\sqrt{73}+20}{2}$$

20+4\sqrt{73} ni 2 ga bo'lish.

$$x=2\sqrt{73}+10$$

x=\frac{20±4\sqrt{73}}{2} tenglamasini yeching, bunda ± manfiy. 20 dan 4\sqrt{73} ni ayirish.

$$x=\frac{20-4\sqrt{73}}{2}$$

20-4\sqrt{73} ni 2 ga bo'lish.

$$x=10-2\sqrt{73}$$

Tenglama yechildi.

$$x=2\sqrt{73}+10 x=10-2\sqrt{73}$$

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.

$$x^{2}-20x-192=0$$

192 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-20x-192-\left(-192\right)=-\left(-192\right)$$

O‘zidan -192 ayirilsa 0 qoladi.

$$x^{2}-20x=-\left(-192\right)$$

0 dan -192 ni ayirish.

$$x^{2}-20x=192$$

-20 ni bo‘lish, x shartining koeffitsienti, 2 ga -10 olish uchun. Keyin, -10 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-20x+\left(-10\right)^{2}=192+\left(-10\right)^{2}$$

-10 kvadratini chiqarish.

$$x^{2}-20x+100=192+100$$

192 ni 100 ga qo'shish.

$$x^{2}-20x+100=292$$

x^{2}-20x+100 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-10\right)^{2}=292$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-10\right)^{2}}=\sqrt{292}$$

Qisqartirish.

$$x-10=2\sqrt{73} x-10=-2\sqrt{73}$$

10 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2\sqrt{73}+10 x=10-2\sqrt{73}$$