x^2-6x-10=0 eching

$$x ^ { 2 } - 6 x - 10 = 0$$

x uchun yechish

$$x=\sqrt{19}+3\approx 7,358898944$$

$$x=3-\sqrt{19}\approx -1,358898944$$

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.

$$x^{2}-6x-10=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -6 ni b va -10 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-10\right)}}{2}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-10\right)}}{2}$$

-4 ni -10 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+40}}{2}$$

36 ni 40 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{76}}{2}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±2\sqrt{19}}{2}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±2\sqrt{19}}{2}$$

x=\frac{6±2\sqrt{19}}{2} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}+6}{2}$$

6+2\sqrt{19} ni 2 ga bo'lish.

$$x=\sqrt{19}+3$$

x=\frac{6±2\sqrt{19}}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{19} ni ayirish.

$$x=\frac{6-2\sqrt{19}}{2}$$

6-2\sqrt{19} ni 2 ga bo'lish.

$$x=3-\sqrt{19}$$

Tenglama yechildi.

$$x=\sqrt{19}+3 x=3-\sqrt{19}$$

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.

$$x^{2}-6x-10=0$$

10 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-6x-10-\left(-10\right)=-\left(-10\right)$$

O‘zidan -10 ayirilsa 0 qoladi.

$$x^{2}-6x=-\left(-10\right)$$

0 dan -10 ni ayirish.

$$x^{2}-6x=10$$

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-6x+\left(-3\right)^{2}=10+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=10+9$$

10 ni 9 ga qo'shish.

$$x^{2}-6x+9=19$$

x^{2}-6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-3\right)^{2}=19$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{19}$$

Qisqartirish.

$$x-3=\sqrt{19} x-3=-\sqrt{19}$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{19}+3 x=3-\sqrt{19}$$