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x^{2}+6x=6
x^{2} hosil qilish uchun x va x ni ko'paytirish.
x^{2}+6x-6=0
Ikkala tarafdan 6 ni ayirish.
x=\frac{-6±\sqrt{6^{2}-4\left(-6\right)}}{2}
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 -6 ni c bilan almashtiring.
x=\frac{-6±\sqrt{36-4\left(-6\right)}}{2}
6 kvadratini chiqarish.
x=\frac{-6±\sqrt{36+24}}{2}
-4 ni -6 marotabaga ko'paytirish.
x=\frac{-6±\sqrt{60}}{2}
36 ni 24 ga qo'shish.
x=\frac{-6±2\sqrt{15}}{2}
60 ning kvadrat ildizini chiqarish.
x=\frac{2\sqrt{15}-6}{2}
x=\frac{-6±2\sqrt{15}}{2} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{15} ga qo'shish.
x=\sqrt{15}-3
-6+2\sqrt{15} ni 2 ga bo'lish.
x=\frac{-2\sqrt{15}-6}{2}
x=\frac{-6±2\sqrt{15}}{2} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{15} ni ayirish.
x=-\sqrt{15}-3
-6-2\sqrt{15} ni 2 ga bo'lish.
x=\sqrt{15}-3 x=-\sqrt{15}-3
Tenglama yechildi.
x^{2}+6x=6
x^{2} hosil qilish uchun x va x ni ko'paytirish.
x^{2}+6x+3^{2}=6+3^{2}
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+9=6+9
3 kvadratini chiqarish.
x^{2}+6x+9=15
6 ni 9 ga qo'shish.
\left(x+3\right)^{2}=15
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.
\sqrt{\left(x+3\right)^{2}}=\sqrt{15}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+3=\sqrt{15} x+3=-\sqrt{15}
Qisqartirish.
x=\sqrt{15}-3 x=-\sqrt{15}-3
Tenglamaning ikkala tarafidan 3 ni ayirish.
x^{2}+6x=6
x^{2} hosil qilish uchun x va x ni ko'paytirish.
x^{2}+6x-6=0
Ikkala tarafdan 6 ni ayirish.
x=\frac{-6±\sqrt{6^{2}-4\left(-6\right)}}{2}
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 -6 ni c bilan almashtiring.
x=\frac{-6±\sqrt{36-4\left(-6\right)}}{2}
6 kvadratini chiqarish.
x=\frac{-6±\sqrt{36+24}}{2}
-4 ni -6 marotabaga ko'paytirish.
x=\frac{-6±\sqrt{60}}{2}
36 ni 24 ga qo'shish.
x=\frac{-6±2\sqrt{15}}{2}
60 ning kvadrat ildizini chiqarish.
x=\frac{2\sqrt{15}-6}{2}
x=\frac{-6±2\sqrt{15}}{2} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{15} ga qo'shish.
x=\sqrt{15}-3
-6+2\sqrt{15} ni 2 ga bo'lish.
x=\frac{-2\sqrt{15}-6}{2}
x=\frac{-6±2\sqrt{15}}{2} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{15} ni ayirish.
x=-\sqrt{15}-3
-6-2\sqrt{15} ni 2 ga bo'lish.
x=\sqrt{15}-3 x=-\sqrt{15}-3
Tenglama yechildi.
x^{2}+6x=6
x^{2} hosil qilish uchun x va x ni ko'paytirish.
x^{2}+6x+3^{2}=6+3^{2}
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+9=6+9
3 kvadratini chiqarish.
x^{2}+6x+9=15
6 ni 9 ga qo'shish.
\left(x+3\right)^{2}=15
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.
\sqrt{\left(x+3\right)^{2}}=\sqrt{15}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+3=\sqrt{15} x+3=-\sqrt{15}
Qisqartirish.
x=\sqrt{15}-3 x=-\sqrt{15}-3
Tenglamaning ikkala tarafidan 3 ni ayirish.