x^2-15x+6=0 eching

$$x ^ { 2 } - 15 x + 6 = 0$$

x uchun yechish

$$x = \frac{\sqrt{201} + 15}{2} \approx 14,588723439$$

$$x=\frac{15-\sqrt{201}}{2}\approx 0,411276561$$

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.

$$x^{2}-15x+6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -15 ni b va 6 ni c bilan almashtiring.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 6}}{2}$$

-15 kvadratini chiqarish.

$$x=\frac{-\left(-15\right)±\sqrt{225-4\times 6}}{2}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-15\right)±\sqrt{225-24}}{2}$$

225 ni -24 ga qo'shish.

$$x=\frac{-\left(-15\right)±\sqrt{201}}{2}$$

-15 ning teskarisi 15 ga teng.

$$x=\frac{15±\sqrt{201}}{2}$$

x=\frac{15±\sqrt{201}}{2} tenglamasini yeching, bunda ± musbat. 15 ni \sqrt{201} ga qo'shish.

$$x=\frac{\sqrt{201}+15}{2}$$

x=\frac{15±\sqrt{201}}{2} tenglamasini yeching, bunda ± manfiy. 15 dan \sqrt{201} ni ayirish.

$$x=\frac{15-\sqrt{201}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{201}+15}{2} x=\frac{15-\sqrt{201}}{2}$$

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.

$$x^{2}-15x+6=0$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$x^{2}-15x+6-6=-6$$

O‘zidan 6 ayirilsa 0 qoladi.

$$x^{2}-15x=-6$$

-15 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{15}{2} olish uchun. Keyin, -\frac{15}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-15x+\left(-\frac{15}{2}\right)^{2}=-6+\left(-\frac{15}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{15}{2} kvadratini chiqarish.

$$x^{2}-15x+\frac{225}{4}=-6+\frac{225}{4}$$

-6 ni \frac{225}{4} ga qo'shish.

$$x^{2}-15x+\frac{225}{4}=\frac{201}{4}$$

x^{2}-15x+\frac{225}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{15}{2}\right)^{2}=\frac{201}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{15}{2}\right)^{2}}=\sqrt{\frac{201}{4}}$$

Qisqartirish.

$$x-\frac{15}{2}=\frac{\sqrt{201}}{2} x-\frac{15}{2}=-\frac{\sqrt{201}}{2}$$

\frac{15}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{201}+15}{2} x=\frac{15-\sqrt{201}}{2}$$