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x\times 45-xx=5
x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.
x\times 45-x^{2}=5
x^{2} hosil qilish uchun x va x ni ko'paytirish.
x\times 45-x^{2}-5=0
Ikkala tarafdan 5 ni ayirish.
-x^{2}+45x-5=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{-45±\sqrt{45^{2}-4\left(-1\right)\left(-5\right)}}{2\left(-1\right)}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 45 ni b va -5 ni c bilan almashtiring.
x=\frac{-45±\sqrt{2025-4\left(-1\right)\left(-5\right)}}{2\left(-1\right)}
45 kvadratini chiqarish.
x=\frac{-45±\sqrt{2025+4\left(-5\right)}}{2\left(-1\right)}
-4 ni -1 marotabaga ko'paytirish.
x=\frac{-45±\sqrt{2025-20}}{2\left(-1\right)}
4 ni -5 marotabaga ko'paytirish.
x=\frac{-45±\sqrt{2005}}{2\left(-1\right)}
2025 ni -20 ga qo'shish.
x=\frac{-45±\sqrt{2005}}{-2}
2 ni -1 marotabaga ko'paytirish.
x=\frac{\sqrt{2005}-45}{-2}
x=\frac{-45±\sqrt{2005}}{-2} tenglamasini yeching, bunda ± musbat. -45 ni \sqrt{2005} ga qo'shish.
x=\frac{45-\sqrt{2005}}{2}
-45+\sqrt{2005} ni -2 ga bo'lish.
x=\frac{-\sqrt{2005}-45}{-2}
x=\frac{-45±\sqrt{2005}}{-2} tenglamasini yeching, bunda ± manfiy. -45 dan \sqrt{2005} ni ayirish.
x=\frac{\sqrt{2005}+45}{2}
-45-\sqrt{2005} ni -2 ga bo'lish.
x=\frac{45-\sqrt{2005}}{2} x=\frac{\sqrt{2005}+45}{2}
Tenglama yechildi.
x\times 45-xx=5
x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.
x\times 45-x^{2}=5
x^{2} hosil qilish uchun x va x ni ko'paytirish.
-x^{2}+45x=5
Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.
\frac{-x^{2}+45x}{-1}=\frac{5}{-1}
Ikki tarafini -1 ga bo‘ling.
x^{2}+\frac{45}{-1}x=\frac{5}{-1}
-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.
x^{2}-45x=\frac{5}{-1}
45 ni -1 ga bo'lish.
x^{2}-45x=-5
5 ni -1 ga bo'lish.
x^{2}-45x+\left(-\frac{45}{2}\right)^{2}=-5+\left(-\frac{45}{2}\right)^{2}
-45 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{45}{2} olish uchun. Keyin, -\frac{45}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}-45x+\frac{2025}{4}=-5+\frac{2025}{4}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{45}{2} kvadratini chiqarish.
x^{2}-45x+\frac{2025}{4}=\frac{2005}{4}
-5 ni \frac{2025}{4} ga qo'shish.
\left(x-\frac{45}{2}\right)^{2}=\frac{2005}{4}
x^{2}-45x+\frac{2025}{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{45}{2}\right)^{2}}=\sqrt{\frac{2005}{4}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-\frac{45}{2}=\frac{\sqrt{2005}}{2} x-\frac{45}{2}=-\frac{\sqrt{2005}}{2}
Qisqartirish.
x=\frac{\sqrt{2005}+45}{2} x=\frac{45-\sqrt{2005}}{2}
\frac{45}{2} ni tenglamaning ikkala tarafiga qo'shish.