x^2+60x-6400=0 eching

$${ x }^{ 2 } +60x-6400=0$$

x uchun yechish

$$x=10\sqrt{73}-30\approx 55,440037453$$

$$x=-10\sqrt{73}-30\approx -115,440037453$$

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.

$$x^{2}+60x-6400=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 60 ni b va -6400 ni c bilan almashtiring.

$$x=\frac{-60±\sqrt{60^{2}-4\left(-6400\right)}}{2}$$

60 kvadratini chiqarish.

$$x=\frac{-60±\sqrt{3600-4\left(-6400\right)}}{2}$$

-4 ni -6400 marotabaga ko'paytirish.

$$x=\frac{-60±\sqrt{3600+25600}}{2}$$

3600 ni 25600 ga qo'shish.

$$x=\frac{-60±\sqrt{29200}}{2}$$

29200 ning kvadrat ildizini chiqarish.

$$x=\frac{-60±20\sqrt{73}}{2}$$

x=\frac{-60±20\sqrt{73}}{2} tenglamasini yeching, bunda ± musbat. -60 ni 20\sqrt{73} ga qo'shish.

$$x=\frac{20\sqrt{73}-60}{2}$$

-60+20\sqrt{73} ni 2 ga bo'lish.

$$x=10\sqrt{73}-30$$

x=\frac{-60±20\sqrt{73}}{2} tenglamasini yeching, bunda ± manfiy. -60 dan 20\sqrt{73} ni ayirish.

$$x=\frac{-20\sqrt{73}-60}{2}$$

-60-20\sqrt{73} ni 2 ga bo'lish.

$$x=-10\sqrt{73}-30$$

Tenglama yechildi.

$$x=10\sqrt{73}-30 x=-10\sqrt{73}-30$$

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.

$$x^{2}+60x-6400=0$$

6400 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+60x-6400-\left(-6400\right)=-\left(-6400\right)$$

O‘zidan -6400 ayirilsa 0 qoladi.

$$x^{2}+60x=-\left(-6400\right)$$

0 dan -6400 ni ayirish.

$$x^{2}+60x=6400$$

60 ni bo‘lish, x shartining koeffitsienti, 2 ga 30 olish uchun. Keyin, 30 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+60x+30^{2}=6400+30^{2}$$

30 kvadratini chiqarish.

$$x^{2}+60x+900=6400+900$$

6400 ni 900 ga qo'shish.

$$x^{2}+60x+900=7300$$

x^{2}+60x+900 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+30\right)^{2}=7300$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+30\right)^{2}}=\sqrt{7300}$$

Qisqartirish.

$$x+30=10\sqrt{73} x+30=-10\sqrt{73}$$

Tenglamaning ikkala tarafidan 30 ni ayirish.

$$x=10\sqrt{73}-30 x=-10\sqrt{73}-30$$