x uchun yechish
x=\frac{3\sqrt{5}-9}{2}\approx -1,145898034
x=\frac{-3\sqrt{5}-9}{2}\approx -7,854101966
Grafik
Baham ko'rish
Klipbordga nusxa olish
x^{2}+9x+9=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.
x=\frac{-9±\sqrt{9^{2}-4\times 9}}{2}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 9 ni b va 9 ni c bilan almashtiring.
x=\frac{-9±\sqrt{81-4\times 9}}{2}
9 kvadratini chiqarish.
x=\frac{-9±\sqrt{81-36}}{2}
-4 ni 9 marotabaga ko'paytirish.
x=\frac{-9±\sqrt{45}}{2}
81 ni -36 ga qo'shish.
x=\frac{-9±3\sqrt{5}}{2}
45 ning kvadrat ildizini chiqarish.
x=\frac{3\sqrt{5}-9}{2}
x=\frac{-9±3\sqrt{5}}{2} tenglamasini yeching, bunda ± musbat. -9 ni 3\sqrt{5} ga qo'shish.
x=\frac{-3\sqrt{5}-9}{2}
x=\frac{-9±3\sqrt{5}}{2} tenglamasini yeching, bunda ± manfiy. -9 dan 3\sqrt{5} ni ayirish.
x=\frac{3\sqrt{5}-9}{2} x=\frac{-3\sqrt{5}-9}{2}
Tenglama yechildi.
x^{2}+9x+9=0
Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.
x^{2}+9x+9-9=-9
Tenglamaning ikkala tarafidan 9 ni ayirish.
x^{2}+9x=-9
O‘zidan 9 ayirilsa 0 qoladi.
x^{2}+9x+\left(\frac{9}{2}\right)^{2}=-9+\left(\frac{9}{2}\right)^{2}
9 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{9}{2} olish uchun. Keyin, \frac{9}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}+9x+\frac{81}{4}=-9+\frac{81}{4}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{9}{2} kvadratini chiqarish.
x^{2}+9x+\frac{81}{4}=\frac{45}{4}
-9 ni \frac{81}{4} ga qo'shish.
\left(x+\frac{9}{2}\right)^{2}=\frac{45}{4}
x^{2}+9x+\frac{81}{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+\frac{9}{2}\right)^{2}}=\sqrt{\frac{45}{4}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x+\frac{9}{2}=\frac{3\sqrt{5}}{2} x+\frac{9}{2}=-\frac{3\sqrt{5}}{2}
Qisqartirish.
x=\frac{3\sqrt{5}-9}{2} x=\frac{-3\sqrt{5}-9}{2}
Tenglamaning ikkala tarafidan \frac{9}{2} ni ayirish.
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}