x^2-28x+48=0 eching

$$x ^ { 2 } - 28 x + 48 = 0$$

x uchun yechish

$$x=2\sqrt{37}+14\approx 26,165525061$$

$$x=14-2\sqrt{37}\approx 1,834474939$$

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.

$$x^{2}-28x+48=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -28 ni b va 48 ni c bilan almashtiring.

$$x=\frac{-\left(-28\right)±\sqrt{\left(-28\right)^{2}-4\times 48}}{2}$$

-28 kvadratini chiqarish.

$$x=\frac{-\left(-28\right)±\sqrt{784-4\times 48}}{2}$$

-4 ni 48 marotabaga ko'paytirish.

$$x=\frac{-\left(-28\right)±\sqrt{784-192}}{2}$$

784 ni -192 ga qo'shish.

$$x=\frac{-\left(-28\right)±\sqrt{592}}{2}$$

592 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-28\right)±4\sqrt{37}}{2}$$

-28 ning teskarisi 28 ga teng.

$$x=\frac{28±4\sqrt{37}}{2}$$

x=\frac{28±4\sqrt{37}}{2} tenglamasini yeching, bunda ± musbat. 28 ni 4\sqrt{37} ga qo'shish.

$$x=\frac{4\sqrt{37}+28}{2}$$

28+4\sqrt{37} ni 2 ga bo'lish.

$$x=2\sqrt{37}+14$$

x=\frac{28±4\sqrt{37}}{2} tenglamasini yeching, bunda ± manfiy. 28 dan 4\sqrt{37} ni ayirish.

$$x=\frac{28-4\sqrt{37}}{2}$$

28-4\sqrt{37} ni 2 ga bo'lish.

$$x=14-2\sqrt{37}$$

Tenglama yechildi.

$$x=2\sqrt{37}+14 x=14-2\sqrt{37}$$

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.

$$x^{2}-28x+48=0$$

Tenglamaning ikkala tarafidan 48 ni ayirish.

$$x^{2}-28x+48-48=-48$$

O‘zidan 48 ayirilsa 0 qoladi.

$$x^{2}-28x=-48$$

-28 ni bo‘lish, x shartining koeffitsienti, 2 ga -14 olish uchun. Keyin, -14 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-28x+\left(-14\right)^{2}=-48+\left(-14\right)^{2}$$

-14 kvadratini chiqarish.

$$x^{2}-28x+196=-48+196$$

-48 ni 196 ga qo'shish.

$$x^{2}-28x+196=148$$

x^{2}-28x+196 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-14\right)^{2}=148$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-14\right)^{2}}=\sqrt{148}$$

Qisqartirish.

$$x-14=2\sqrt{37} x-14=-2\sqrt{37}$$

14 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2\sqrt{37}+14 x=14-2\sqrt{37}$$