x^2-45x-700=0 eching

$${ x }^{ 2 } -45x-700=0$$

x uchun yechish

$$x = \frac{5 \sqrt{193} + 45}{2} \approx 57,231109974$$

$$x=\frac{45-5\sqrt{193}}{2}\approx -12,231109974$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$x^{2}-45x-700=0$$

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 -700 ni c bilan almashtiring.

$$x=\frac{-\left(-45\right)±\sqrt{\left(-45\right)^{2}-4\left(-700\right)}}{2}$$

-45 kvadratini chiqarish.

$$x=\frac{-\left(-45\right)±\sqrt{2025-4\left(-700\right)}}{2}$$

-4 ni -700 marotabaga ko'paytirish.

$$x=\frac{-\left(-45\right)±\sqrt{2025+2800}}{2}$$

2025 ni 2800 ga qo'shish.

$$x=\frac{-\left(-45\right)±\sqrt{4825}}{2}$$

4825 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-45\right)±5\sqrt{193}}{2}$$

-45 ning teskarisi 45 ga teng.

$$x=\frac{45±5\sqrt{193}}{2}$$

x=\frac{45±5\sqrt{193}}{2} tenglamasini yeching, bunda ± musbat. 45 ni 5\sqrt{193} ga qo'shish.

$$x=\frac{5\sqrt{193}+45}{2}$$

x=\frac{45±5\sqrt{193}}{2} tenglamasini yeching, bunda ± manfiy. 45 dan 5\sqrt{193} ni ayirish.

$$x=\frac{45-5\sqrt{193}}{2}$$

Tenglama yechildi.

$$x=\frac{5\sqrt{193}+45}{2} x=\frac{45-5\sqrt{193}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}-45x-700=0$$

700 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-45x-700-\left(-700\right)=-\left(-700\right)$$

O‘zidan -700 ayirilsa 0 qoladi.

$$x^{2}-45x=-\left(-700\right)$$

0 dan -700 ni ayirish.

$$x^{2}-45x=700$$

-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.

$$x^{2}-45x+\left(-\frac{45}{2}\right)^{2}=700+\left(-\frac{45}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{45}{2} kvadratini chiqarish.

$$x^{2}-45x+\frac{2025}{4}=700+\frac{2025}{4}$$

700 ni \frac{2025}{4} ga qo'shish.

$$x^{2}-45x+\frac{2025}{4}=\frac{4825}{4}$$

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.

$$\left(x-\frac{45}{2}\right)^{2}=\frac{4825}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{45}{2}\right)^{2}}=\sqrt{\frac{4825}{4}}$$

Qisqartirish.

$$x-\frac{45}{2}=\frac{5\sqrt{193}}{2} x-\frac{45}{2}=-\frac{5\sqrt{193}}{2}$$

\frac{45}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{5\sqrt{193}+45}{2} x=\frac{45-5\sqrt{193}}{2}$$