x^2+6x-10=0 eching

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

x uchun yechish (complex solution)

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

$$x=-\left(\sqrt{19}+3\right)\approx -7,358898944$$

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.

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

6 kvadratini chiqarish.

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

-4 ni -10 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+40}}{2}$$

36 ni 40 ga qo'shish.

$$x=\frac{-6±\sqrt{76}}{2}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{19}}{2}$$

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.

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

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

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

Tenglama yechildi.

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

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.

$$x^{2}+6x+3^{2}=10+3^{2}$$

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.

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

Tenglamaning ikkala tarafidan 3 ni ayirish.

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

x uchun yechish

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

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

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.

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

6 kvadratini chiqarish.

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

-4 ni -10 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+40}}{2}$$

36 ni 40 ga qo'shish.

$$x=\frac{-6±\sqrt{76}}{2}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{19}}{2}$$

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.

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

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

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

Tenglama yechildi.

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

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.

$$x^{2}+6x+3^{2}=10+3^{2}$$

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.

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

Tenglamaning ikkala tarafidan 3 ni ayirish.

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