60x=x^2 eching

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

x uchun yechish

$$x=60$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan x^{2} ni ayirish.

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

x omili.

$$x\left(60-x\right)=0$$

Tenglamani yechish uchun x=0 va 60-x=0 ni yeching.

$$x=0 x=60$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan x^{2} ni ayirish.

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

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.

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

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 0 ni c bilan almashtiring.

$$x=\frac{-60±\sqrt{60^{2}}}{2\left(-1\right)}$$

60^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-60±60}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-60±60}{-2}$$

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

$$x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$x=0$$

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

$$x=-\frac{120}{-2}$$

-120 ni -2 ga bo'lish.

$$x=60$$

Tenglama yechildi.

$$x=0 x=60$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan x^{2} ni ayirish.

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

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

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

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+60x}{-1}=\frac{0}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{60}{-1}x=\frac{0}{-1}$$

60 ni -1 ga bo'lish.

$$x^{2}-60x=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

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

-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.

$$x^{2}-60x+\left(-30\right)^{2}=\left(-30\right)^{2}$$

-30 kvadratini chiqarish.

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

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.

$$\left(x-30\right)^{2}=900$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-30\right)^{2}}=\sqrt{900}$$

Qisqartirish.

$$x-30=30 x-30=-30$$

30 ni tenglamaning ikkala tarafiga qo'shish.

$$x=60 x=0$$