x^2-20=55x eching

$${ x }^{ 2 } -20 = 55x$$

x uchun yechish

$$x = \frac{3 \sqrt{345} + 55}{2} \approx 55,361263432$$

$$x=\frac{55-3\sqrt{345}}{2}\approx -0,361263432$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 55x ni ayirish.

$$x^{2}-20-55x=0$$

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.

$$x^{2}-55x-20=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -55 ni b va -20 ni c bilan almashtiring.

$$x=\frac{-\left(-55\right)±\sqrt{\left(-55\right)^{2}-4\left(-20\right)}}{2}$$

-55 kvadratini chiqarish.

$$x=\frac{-\left(-55\right)±\sqrt{3025-4\left(-20\right)}}{2}$$

-4 ni -20 marotabaga ko'paytirish.

$$x=\frac{-\left(-55\right)±\sqrt{3025+80}}{2}$$

3025 ni 80 ga qo'shish.

$$x=\frac{-\left(-55\right)±\sqrt{3105}}{2}$$

3105 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-55\right)±3\sqrt{345}}{2}$$

-55 ning teskarisi 55 ga teng.

$$x=\frac{55±3\sqrt{345}}{2}$$

x=\frac{55±3\sqrt{345}}{2} tenglamasini yeching, bunda ± musbat. 55 ni 3\sqrt{345} ga qo'shish.

$$x=\frac{3\sqrt{345}+55}{2}$$

x=\frac{55±3\sqrt{345}}{2} tenglamasini yeching, bunda ± manfiy. 55 dan 3\sqrt{345} ni ayirish.

$$x=\frac{55-3\sqrt{345}}{2}$$

Tenglama yechildi.

$$x=\frac{3\sqrt{345}+55}{2} x=\frac{55-3\sqrt{345}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 55x ni ayirish.

$$x^{2}-20-55x=0$$

20 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}-55x=20$$

-55 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{55}{2} olish uchun. Keyin, -\frac{55}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-55x+\left(-\frac{55}{2}\right)^{2}=20+\left(-\frac{55}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{55}{2} kvadratini chiqarish.

$$x^{2}-55x+\frac{3025}{4}=20+\frac{3025}{4}$$

20 ni \frac{3025}{4} ga qo'shish.

$$x^{2}-55x+\frac{3025}{4}=\frac{3105}{4}$$

x^{2}-55x+\frac{3025}{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.

$$\left(x-\frac{55}{2}\right)^{2}=\frac{3105}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{55}{2}\right)^{2}}=\sqrt{\frac{3105}{4}}$$

Qisqartirish.

$$x-\frac{55}{2}=\frac{3\sqrt{345}}{2} x-\frac{55}{2}=-\frac{3\sqrt{345}}{2}$$

\frac{55}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3\sqrt{345}+55}{2} x=\frac{55-3\sqrt{345}}{2}$$