c uchun yechish
c=4+\sqrt{3}i\approx 4+1,732050808i
c=-\sqrt{3}i+4\approx 4-1,732050808i
Baham ko'rish
Klipbordga nusxa olish
c^{2}-8c+19=0
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.
c=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 19}}{2}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -8 ni b va 19 ni c bilan almashtiring.
c=\frac{-\left(-8\right)±\sqrt{64-4\times 19}}{2}
-8 kvadratini chiqarish.
c=\frac{-\left(-8\right)±\sqrt{64-76}}{2}
-4 ni 19 marotabaga ko'paytirish.
c=\frac{-\left(-8\right)±\sqrt{-12}}{2}
64 ni -76 ga qo'shish.
c=\frac{-\left(-8\right)±2\sqrt{3}i}{2}
-12 ning kvadrat ildizini chiqarish.
c=\frac{8±2\sqrt{3}i}{2}
-8 ning teskarisi 8 ga teng.
c=\frac{8+2\sqrt{3}i}{2}
c=\frac{8±2\sqrt{3}i}{2} tenglamasini yeching, bunda ± musbat. 8 ni 2i\sqrt{3} ga qo'shish.
c=4+\sqrt{3}i
8+2i\sqrt{3} ni 2 ga bo'lish.
c=\frac{-2\sqrt{3}i+8}{2}
c=\frac{8±2\sqrt{3}i}{2} tenglamasini yeching, bunda ± manfiy. 8 dan 2i\sqrt{3} ni ayirish.
c=-\sqrt{3}i+4
8-2i\sqrt{3} ni 2 ga bo'lish.
c=4+\sqrt{3}i c=-\sqrt{3}i+4
Tenglama yechildi.
c^{2}-8c+19=0
Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.
c^{2}-8c+19-19=-19
Tenglamaning ikkala tarafidan 19 ni ayirish.
c^{2}-8c=-19
O‘zidan 19 ayirilsa 0 qoladi.
c^{2}-8c+\left(-4\right)^{2}=-19+\left(-4\right)^{2}
-8 ni bo‘lish, x shartining koeffitsienti, 2 ga -4 olish uchun. Keyin, -4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
c^{2}-8c+16=-19+16
-4 kvadratini chiqarish.
c^{2}-8c+16=-3
-19 ni 16 ga qo'shish.
\left(c-4\right)^{2}=-3
c^{2}-8c+16 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(c-4\right)^{2}}=\sqrt{-3}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
c-4=\sqrt{3}i c-4=-\sqrt{3}i
Qisqartirish.
c=4+\sqrt{3}i c=-\sqrt{3}i+4
4 ni tenglamaning ikkala tarafiga qo'shish.
Misollar
Ikkilik tenglama
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometriya
4 \sin \theta \cos \theta = 2 \sin \theta
Chiziqli tenglama
y = 3x + 4
Arifmetik
699 * 533
Matritsa
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simli tenglama
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differensatsiya
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Oʻngga
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Chegaralar
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}