x^2+52x-45=0 eching

$${ x }^{ 2 } +52x-45=0$$

x uchun yechish (complex solution)

$$x=\sqrt{721}-26\approx 0,851443164$$

$$x=-\left(\sqrt{721}+26\right)\approx -52,851443164$$

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.

$$x^{2}+52x-45=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 52 ni b va -45 ni c bilan almashtiring.

$$x=\frac{-52±\sqrt{52^{2}-4\left(-45\right)}}{2}$$

52 kvadratini chiqarish.

$$x=\frac{-52±\sqrt{2704-4\left(-45\right)}}{2}$$

-4 ni -45 marotabaga ko'paytirish.

$$x=\frac{-52±\sqrt{2704+180}}{2}$$

2704 ni 180 ga qo'shish.

$$x=\frac{-52±\sqrt{2884}}{2}$$

2884 ning kvadrat ildizini chiqarish.

$$x=\frac{-52±2\sqrt{721}}{2}$$

x=\frac{-52±2\sqrt{721}}{2} tenglamasini yeching, bunda ± musbat. -52 ni 2\sqrt{721} ga qo'shish.

$$x=\frac{2\sqrt{721}-52}{2}$$

-52+2\sqrt{721} ni 2 ga bo'lish.

$$x=\sqrt{721}-26$$

x=\frac{-52±2\sqrt{721}}{2} tenglamasini yeching, bunda ± manfiy. -52 dan 2\sqrt{721} ni ayirish.

$$x=\frac{-2\sqrt{721}-52}{2}$$

-52-2\sqrt{721} ni 2 ga bo'lish.

$$x=-\sqrt{721}-26$$

Tenglama yechildi.

$$x=\sqrt{721}-26 x=-\sqrt{721}-26$$

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.

$$x^{2}+52x-45=0$$

45 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+52x-45-\left(-45\right)=-\left(-45\right)$$

O‘zidan -45 ayirilsa 0 qoladi.

$$x^{2}+52x=-\left(-45\right)$$

0 dan -45 ni ayirish.

$$x^{2}+52x=45$$

52 ni bo‘lish, x shartining koeffitsienti, 2 ga 26 olish uchun. Keyin, 26 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+52x+26^{2}=45+26^{2}$$

26 kvadratini chiqarish.

$$x^{2}+52x+676=45+676$$

45 ni 676 ga qo'shish.

$$x^{2}+52x+676=721$$

x^{2}+52x+676 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+26\right)^{2}=721$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+26\right)^{2}}=\sqrt{721}$$

Qisqartirish.

$$x+26=\sqrt{721} x+26=-\sqrt{721}$$

Tenglamaning ikkala tarafidan 26 ni ayirish.

$$x=\sqrt{721}-26 x=-\sqrt{721}-26$$

x uchun yechish

$$x=\sqrt{721}-26\approx 0,851443164$$

$$x=-\sqrt{721}-26\approx -52,851443164$$

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.

$$x^{2}+52x-45=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 52 ni b va -45 ni c bilan almashtiring.

$$x=\frac{-52±\sqrt{52^{2}-4\left(-45\right)}}{2}$$

52 kvadratini chiqarish.

$$x=\frac{-52±\sqrt{2704-4\left(-45\right)}}{2}$$

-4 ni -45 marotabaga ko'paytirish.

$$x=\frac{-52±\sqrt{2704+180}}{2}$$

2704 ni 180 ga qo'shish.

$$x=\frac{-52±\sqrt{2884}}{2}$$

2884 ning kvadrat ildizini chiqarish.

$$x=\frac{-52±2\sqrt{721}}{2}$$

x=\frac{-52±2\sqrt{721}}{2} tenglamasini yeching, bunda ± musbat. -52 ni 2\sqrt{721} ga qo'shish.

$$x=\frac{2\sqrt{721}-52}{2}$$

-52+2\sqrt{721} ni 2 ga bo'lish.

$$x=\sqrt{721}-26$$

x=\frac{-52±2\sqrt{721}}{2} tenglamasini yeching, bunda ± manfiy. -52 dan 2\sqrt{721} ni ayirish.

$$x=\frac{-2\sqrt{721}-52}{2}$$

-52-2\sqrt{721} ni 2 ga bo'lish.

$$x=-\sqrt{721}-26$$

Tenglama yechildi.

$$x=\sqrt{721}-26 x=-\sqrt{721}-26$$

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.

$$x^{2}+52x-45=0$$

45 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+52x-45-\left(-45\right)=-\left(-45\right)$$

O‘zidan -45 ayirilsa 0 qoladi.

$$x^{2}+52x=-\left(-45\right)$$

0 dan -45 ni ayirish.

$$x^{2}+52x=45$$

52 ni bo‘lish, x shartining koeffitsienti, 2 ga 26 olish uchun. Keyin, 26 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+52x+26^{2}=45+26^{2}$$

26 kvadratini chiqarish.

$$x^{2}+52x+676=45+676$$

45 ni 676 ga qo'shish.

$$x^{2}+52x+676=721$$

x^{2}+52x+676 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+26\right)^{2}=721$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+26\right)^{2}}=\sqrt{721}$$

Qisqartirish.

$$x+26=\sqrt{721} x+26=-\sqrt{721}$$

Tenglamaning ikkala tarafidan 26 ni ayirish.

$$x=\sqrt{721}-26 x=-\sqrt{721}-26$$