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x^{2}+5x-21=0
Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.
x=\frac{-5±\sqrt{5^{2}-4\left(-21\right)}}{2}
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{-5±\sqrt{25-4\left(-21\right)}}{2}
5 kvadratini chiqarish.
x=\frac{-5±\sqrt{25+84}}{2}
-4 ni -21 marotabaga ko'paytirish.
x=\frac{-5±\sqrt{109}}{2}
25 ni 84 ga qo'shish.
x=\frac{\sqrt{109}-5}{2}
x=\frac{-5±\sqrt{109}}{2} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{109} ga qo'shish.
x=\frac{-\sqrt{109}-5}{2}
x=\frac{-5±\sqrt{109}}{2} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{109} ni ayirish.
x^{2}+5x-21=\left(x-\frac{\sqrt{109}-5}{2}\right)\left(x-\frac{-\sqrt{109}-5}{2}\right)
ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-5+\sqrt{109}}{2} ga va x_{2} uchun \frac{-5-\sqrt{109}}{2} ga bo‘ling.