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x^{2}-9x-600=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{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\left(-600\right)}}{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 -600 ni c bilan almashtiring.
x=\frac{-\left(-9\right)±\sqrt{81-4\left(-600\right)}}{2}
-9 kvadratini chiqarish.
x=\frac{-\left(-9\right)±\sqrt{81+2400}}{2}
-4 ni -600 marotabaga ko'paytirish.
x=\frac{-\left(-9\right)±\sqrt{2481}}{2}
81 ni 2400 ga qo'shish.
x=\frac{9±\sqrt{2481}}{2}
-9 ning teskarisi 9 ga teng.
x=\frac{\sqrt{2481}+9}{2}
x=\frac{9±\sqrt{2481}}{2} tenglamasini yeching, bunda ± musbat. 9 ni \sqrt{2481} ga qo'shish.
x=\frac{9-\sqrt{2481}}{2}
x=\frac{9±\sqrt{2481}}{2} tenglamasini yeching, bunda ± manfiy. 9 dan \sqrt{2481} ni ayirish.
x=\frac{\sqrt{2481}+9}{2} x=\frac{9-\sqrt{2481}}{2}
Tenglama yechildi.
x^{2}-9x-600=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-600-\left(-600\right)=-\left(-600\right)
600 ni tenglamaning ikkala tarafiga qo'shish.
x^{2}-9x=-\left(-600\right)
O‘zidan -600 ayirilsa 0 qoladi.
x^{2}-9x=600
0 dan -600 ni ayirish.
x^{2}-9x+\left(-\frac{9}{2}\right)^{2}=600+\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}=600+\frac{81}{4}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{2} kvadratini chiqarish.
x^{2}-9x+\frac{81}{4}=\frac{2481}{4}
600 ni \frac{81}{4} ga qo'shish.
\left(x-\frac{9}{2}\right)^{2}=\frac{2481}{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{2481}{4}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-\frac{9}{2}=\frac{\sqrt{2481}}{2} x-\frac{9}{2}=-\frac{\sqrt{2481}}{2}
Qisqartirish.
x=\frac{\sqrt{2481}+9}{2} x=\frac{9-\sqrt{2481}}{2}
\frac{9}{2} ni tenglamaning ikkala tarafiga qo'shish.