x^2+85x=550 eching

$$x ^ { 2 } + 85 x = 550$$

x uchun yechish

$$x = \frac{5 \sqrt{377} - 85}{2} \approx 6,041219597$$

$$x=\frac{-5\sqrt{377}-85}{2}\approx -91,041219597$$

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.

$$x^{2}+85x=550$$

Tenglamaning ikkala tarafidan 550 ni ayirish.

$$x^{2}+85x-550=550-550$$

O‘zidan 550 ayirilsa 0 qoladi.

$$x^{2}+85x-550=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 85 ni b va -550 ni c bilan almashtiring.

$$x=\frac{-85±\sqrt{85^{2}-4\left(-550\right)}}{2}$$

85 kvadratini chiqarish.

$$x=\frac{-85±\sqrt{7225-4\left(-550\right)}}{2}$$

-4 ni -550 marotabaga ko'paytirish.

$$x=\frac{-85±\sqrt{7225+2200}}{2}$$

7225 ni 2200 ga qo'shish.

$$x=\frac{-85±\sqrt{9425}}{2}$$

9425 ning kvadrat ildizini chiqarish.

$$x=\frac{-85±5\sqrt{377}}{2}$$

x=\frac{-85±5\sqrt{377}}{2} tenglamasini yeching, bunda ± musbat. -85 ni 5\sqrt{377} ga qo'shish.

$$x=\frac{5\sqrt{377}-85}{2}$$

x=\frac{-85±5\sqrt{377}}{2} tenglamasini yeching, bunda ± manfiy. -85 dan 5\sqrt{377} ni ayirish.

$$x=\frac{-5\sqrt{377}-85}{2}$$

Tenglama yechildi.

$$x=\frac{5\sqrt{377}-85}{2} x=\frac{-5\sqrt{377}-85}{2}$$

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.

$$x^{2}+85x=550$$

85 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{85}{2} olish uchun. Keyin, \frac{85}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+85x+\left(\frac{85}{2}\right)^{2}=550+\left(\frac{85}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{85}{2} kvadratini chiqarish.

$$x^{2}+85x+\frac{7225}{4}=550+\frac{7225}{4}$$

550 ni \frac{7225}{4} ga qo'shish.

$$x^{2}+85x+\frac{7225}{4}=\frac{9425}{4}$$

x^{2}+85x+\frac{7225}{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.

$$\left(x+\frac{85}{2}\right)^{2}=\frac{9425}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{85}{2}\right)^{2}}=\sqrt{\frac{9425}{4}}$$

Qisqartirish.

$$x+\frac{85}{2}=\frac{5\sqrt{377}}{2} x+\frac{85}{2}=-\frac{5\sqrt{377}}{2}$$

Tenglamaning ikkala tarafidan \frac{85}{2} ni ayirish.

$$x=\frac{5\sqrt{377}-85}{2} x=\frac{-5\sqrt{377}-85}{2}$$