x uchun yechish
x=-4
x=0
Grafik
Baham ko'rish
Klipbordga nusxa olish
x^{2}-x-6=\left(3x-2\right)\left(x+3\right)
x+2 ga x-3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.
x^{2}-x-6=3x^{2}+7x-6
3x-2 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.
x^{2}-x-6-3x^{2}=7x-6
Ikkala tarafdan 3x^{2} ni ayirish.
-2x^{2}-x-6=7x-6
-2x^{2} ni olish uchun x^{2} va -3x^{2} ni birlashtirish.
-2x^{2}-x-6-7x=-6
Ikkala tarafdan 7x ni ayirish.
-2x^{2}-8x-6=-6
-8x ni olish uchun -x va -7x ni birlashtirish.
-2x^{2}-8x-6+6=0
6 ni ikki tarafga qo’shing.
-2x^{2}-8x=0
0 olish uchun -6 va 6'ni qo'shing.
x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2\left(-2\right)}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, -8 ni b va 0 ni c bilan almashtiring.
x=\frac{-\left(-8\right)±8}{2\left(-2\right)}
\left(-8\right)^{2} ning kvadrat ildizini chiqarish.
x=\frac{8±8}{2\left(-2\right)}
-8 ning teskarisi 8 ga teng.
x=\frac{8±8}{-4}
2 ni -2 marotabaga ko'paytirish.
x=\frac{16}{-4}
x=\frac{8±8}{-4} tenglamasini yeching, bunda ± musbat. 8 ni 8 ga qo'shish.
x=-4
16 ni -4 ga bo'lish.
x=\frac{0}{-4}
x=\frac{8±8}{-4} tenglamasini yeching, bunda ± manfiy. 8 dan 8 ni ayirish.
x=0
0 ni -4 ga bo'lish.
x=-4 x=0
Tenglama yechildi.
x^{2}-x-6=\left(3x-2\right)\left(x+3\right)
x+2 ga x-3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.
x^{2}-x-6=3x^{2}+7x-6
3x-2 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.
x^{2}-x-6-3x^{2}=7x-6
Ikkala tarafdan 3x^{2} ni ayirish.
-2x^{2}-x-6=7x-6
-2x^{2} ni olish uchun x^{2} va -3x^{2} ni birlashtirish.
-2x^{2}-x-6-7x=-6
Ikkala tarafdan 7x ni ayirish.
-2x^{2}-8x-6=-6
-8x ni olish uchun -x va -7x ni birlashtirish.
-2x^{2}-8x=-6+6
6 ni ikki tarafga qo’shing.
-2x^{2}-8x=0
0 olish uchun -6 va 6'ni qo'shing.
\frac{-2x^{2}-8x}{-2}=\frac{0}{-2}
Ikki tarafini -2 ga bo‘ling.
x^{2}+\left(-\frac{8}{-2}\right)x=\frac{0}{-2}
-2 ga bo'lish -2 ga ko'paytirishni bekor qiladi.
x^{2}+4x=\frac{0}{-2}
-8 ni -2 ga bo'lish.
x^{2}+4x=0
0 ni -2 ga bo'lish.
x^{2}+4x+2^{2}=2^{2}
4 ni bo‘lish, x shartining koeffitsienti, 2 ga 2 olish uchun. Keyin, 2 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}+4x+4=4
2 kvadratini chiqarish.
\left(x+2\right)^{2}=4
x^{2}+4x+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.
\sqrt{\left(x+2\right)^{2}}=\sqrt{4}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+2=2 x+2=-2
Qisqartirish.
x=0 x=-4
Tenglamaning ikkala tarafidan 2 ni ayirish.
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