x^2+54x-5=500 eching

$${ x }^{ 2 } +54x-5=500$$

x uchun yechish (complex solution)

$$x=\sqrt{1234}-27\approx 8,128336141$$

$$x=-\left(\sqrt{1234}+27\right)\approx -62,128336141$$

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.

$$x^{2}+54x-5=500$$

Tenglamaning ikkala tarafidan 500 ni ayirish.

$$x^{2}+54x-5-500=500-500$$

O‘zidan 500 ayirilsa 0 qoladi.

$$x^{2}+54x-5-500=0$$

-5 dan 500 ni ayirish.

$$x^{2}+54x-505=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 54 ni b va -505 ni c bilan almashtiring.

$$x=\frac{-54±\sqrt{54^{2}-4\left(-505\right)}}{2}$$

54 kvadratini chiqarish.

$$x=\frac{-54±\sqrt{2916-4\left(-505\right)}}{2}$$

-4 ni -505 marotabaga ko'paytirish.

$$x=\frac{-54±\sqrt{2916+2020}}{2}$$

2916 ni 2020 ga qo'shish.

$$x=\frac{-54±\sqrt{4936}}{2}$$

4936 ning kvadrat ildizini chiqarish.

$$x=\frac{-54±2\sqrt{1234}}{2}$$

x=\frac{-54±2\sqrt{1234}}{2} tenglamasini yeching, bunda ± musbat. -54 ni 2\sqrt{1234} ga qo'shish.

$$x=\frac{2\sqrt{1234}-54}{2}$$

-54+2\sqrt{1234} ni 2 ga bo'lish.

$$x=\sqrt{1234}-27$$

x=\frac{-54±2\sqrt{1234}}{2} tenglamasini yeching, bunda ± manfiy. -54 dan 2\sqrt{1234} ni ayirish.

$$x=\frac{-2\sqrt{1234}-54}{2}$$

-54-2\sqrt{1234} ni 2 ga bo'lish.

$$x=-\sqrt{1234}-27$$

Tenglama yechildi.

$$x=\sqrt{1234}-27 x=-\sqrt{1234}-27$$

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.

$$x^{2}+54x-5=500$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+54x-5-\left(-5\right)=500-\left(-5\right)$$

O‘zidan -5 ayirilsa 0 qoladi.

$$x^{2}+54x=500-\left(-5\right)$$

500 dan -5 ni ayirish.

$$x^{2}+54x=505$$

54 ni bo‘lish, x shartining koeffitsienti, 2 ga 27 olish uchun. Keyin, 27 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+54x+27^{2}=505+27^{2}$$

27 kvadratini chiqarish.

$$x^{2}+54x+729=505+729$$

505 ni 729 ga qo'shish.

$$x^{2}+54x+729=1234$$

x^{2}+54x+729 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+27\right)^{2}=1234$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+27\right)^{2}}=\sqrt{1234}$$

Qisqartirish.

$$x+27=\sqrt{1234} x+27=-\sqrt{1234}$$

Tenglamaning ikkala tarafidan 27 ni ayirish.

$$x=\sqrt{1234}-27 x=-\sqrt{1234}-27$$

x uchun yechish

$$x=\sqrt{1234}-27\approx 8,128336141$$

$$x=-\sqrt{1234}-27\approx -62,128336141$$

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.

$$x^{2}+54x-5=500$$

Tenglamaning ikkala tarafidan 500 ni ayirish.

$$x^{2}+54x-5-500=500-500$$

O‘zidan 500 ayirilsa 0 qoladi.

$$x^{2}+54x-5-500=0$$

-5 dan 500 ni ayirish.

$$x^{2}+54x-505=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 54 ni b va -505 ni c bilan almashtiring.

$$x=\frac{-54±\sqrt{54^{2}-4\left(-505\right)}}{2}$$

54 kvadratini chiqarish.

$$x=\frac{-54±\sqrt{2916-4\left(-505\right)}}{2}$$

-4 ni -505 marotabaga ko'paytirish.

$$x=\frac{-54±\sqrt{2916+2020}}{2}$$

2916 ni 2020 ga qo'shish.

$$x=\frac{-54±\sqrt{4936}}{2}$$

4936 ning kvadrat ildizini chiqarish.

$$x=\frac{-54±2\sqrt{1234}}{2}$$

x=\frac{-54±2\sqrt{1234}}{2} tenglamasini yeching, bunda ± musbat. -54 ni 2\sqrt{1234} ga qo'shish.

$$x=\frac{2\sqrt{1234}-54}{2}$$

-54+2\sqrt{1234} ni 2 ga bo'lish.

$$x=\sqrt{1234}-27$$

x=\frac{-54±2\sqrt{1234}}{2} tenglamasini yeching, bunda ± manfiy. -54 dan 2\sqrt{1234} ni ayirish.

$$x=\frac{-2\sqrt{1234}-54}{2}$$

-54-2\sqrt{1234} ni 2 ga bo'lish.

$$x=-\sqrt{1234}-27$$

Tenglama yechildi.

$$x=\sqrt{1234}-27 x=-\sqrt{1234}-27$$

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.

$$x^{2}+54x-5=500$$

5 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+54x-5-\left(-5\right)=500-\left(-5\right)$$

O‘zidan -5 ayirilsa 0 qoladi.

$$x^{2}+54x=500-\left(-5\right)$$

500 dan -5 ni ayirish.

$$x^{2}+54x=505$$

54 ni bo‘lish, x shartining koeffitsienti, 2 ga 27 olish uchun. Keyin, 27 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+54x+27^{2}=505+27^{2}$$

27 kvadratini chiqarish.

$$x^{2}+54x+729=505+729$$

505 ni 729 ga qo'shish.

$$x^{2}+54x+729=1234$$

x^{2}+54x+729 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+27\right)^{2}=1234$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+27\right)^{2}}=\sqrt{1234}$$

Qisqartirish.

$$x+27=\sqrt{1234} x+27=-\sqrt{1234}$$

Tenglamaning ikkala tarafidan 27 ni ayirish.

$$x=\sqrt{1234}-27 x=-\sqrt{1234}-27$$