x^2-72x+480=0 eching

$$x ^ { 2 } - 72 x + 480 = 0$$

x uchun yechish

$$x=4\sqrt{51}+36\approx 64,565713714$$

$$x=36-4\sqrt{51}\approx 7,434286286$$

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.

$$x^{2}-72x+480=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -72 ni b va 480 ni c bilan almashtiring.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}-4\times 480}}{2}$$

-72 kvadratini chiqarish.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4\times 480}}{2}$$

-4 ni 480 marotabaga ko'paytirish.

$$x=\frac{-\left(-72\right)±\sqrt{5184-1920}}{2}$$

5184 ni -1920 ga qo'shish.

$$x=\frac{-\left(-72\right)±\sqrt{3264}}{2}$$

3264 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-72\right)±8\sqrt{51}}{2}$$

-72 ning teskarisi 72 ga teng.

$$x=\frac{72±8\sqrt{51}}{2}$$

x=\frac{72±8\sqrt{51}}{2} tenglamasini yeching, bunda ± musbat. 72 ni 8\sqrt{51} ga qo'shish.

$$x=\frac{8\sqrt{51}+72}{2}$$

72+8\sqrt{51} ni 2 ga bo'lish.

$$x=4\sqrt{51}+36$$

x=\frac{72±8\sqrt{51}}{2} tenglamasini yeching, bunda ± manfiy. 72 dan 8\sqrt{51} ni ayirish.

$$x=\frac{72-8\sqrt{51}}{2}$$

72-8\sqrt{51} ni 2 ga bo'lish.

$$x=36-4\sqrt{51}$$

Tenglama yechildi.

$$x=4\sqrt{51}+36 x=36-4\sqrt{51}$$

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.

$$x^{2}-72x+480=0$$

Tenglamaning ikkala tarafidan 480 ni ayirish.

$$x^{2}-72x+480-480=-480$$

O‘zidan 480 ayirilsa 0 qoladi.

$$x^{2}-72x=-480$$

-72 ni bo‘lish, x shartining koeffitsienti, 2 ga -36 olish uchun. Keyin, -36 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-72x+\left(-36\right)^{2}=-480+\left(-36\right)^{2}$$

-36 kvadratini chiqarish.

$$x^{2}-72x+1296=-480+1296$$

-480 ni 1296 ga qo'shish.

$$x^{2}-72x+1296=816$$

x^{2}-72x+1296 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-36\right)^{2}=816$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-36\right)^{2}}=\sqrt{816}$$

Qisqartirish.

$$x-36=4\sqrt{51} x-36=-4\sqrt{51}$$

36 ni tenglamaning ikkala tarafiga qo'shish.

$$x=4\sqrt{51}+36 x=36-4\sqrt{51}$$