-b^2+26+b=0 eching

$$- b ^ { 2 } + 26 + b = 0$$

b uchun yechish

$$b = \frac{\sqrt{105} + 1}{2} \approx 5,623475383$$

$$b=\frac{1-\sqrt{105}}{2}\approx -4,623475383$$

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.

$$-b^{2}+b+26=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 1 ni b va 26 ni c bilan almashtiring.

$$b=\frac{-1±\sqrt{1^{2}-4\left(-1\right)\times 26}}{2\left(-1\right)}$$

1 kvadratini chiqarish.

$$b=\frac{-1±\sqrt{1-4\left(-1\right)\times 26}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$b=\frac{-1±\sqrt{1+4\times 26}}{2\left(-1\right)}$$

4 ni 26 marotabaga ko'paytirish.

$$b=\frac{-1±\sqrt{1+104}}{2\left(-1\right)}$$

1 ni 104 ga qo'shish.

$$b=\frac{-1±\sqrt{105}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$b=\frac{-1±\sqrt{105}}{-2}$$

b=\frac{-1±\sqrt{105}}{-2} tenglamasini yeching, bunda ± musbat. -1 ni \sqrt{105} ga qo'shish.

$$b=\frac{\sqrt{105}-1}{-2}$$

-1+\sqrt{105} ni -2 ga bo'lish.

$$b=\frac{1-\sqrt{105}}{2}$$

b=\frac{-1±\sqrt{105}}{-2} tenglamasini yeching, bunda ± manfiy. -1 dan \sqrt{105} ni ayirish.

$$b=\frac{-\sqrt{105}-1}{-2}$$

-1-\sqrt{105} ni -2 ga bo'lish.

$$b=\frac{\sqrt{105}+1}{2}$$

Tenglama yechildi.

$$b=\frac{1-\sqrt{105}}{2} b=\frac{\sqrt{105}+1}{2}$$

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.

$$-b^{2}+b+26=0$$

Tenglamaning ikkala tarafidan 26 ni ayirish.

$$-b^{2}+b+26-26=-26$$

O‘zidan 26 ayirilsa 0 qoladi.

$$-b^{2}+b=-26$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-b^{2}+b}{-1}=-\frac{26}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$b^{2}+\frac{1}{-1}b=-\frac{26}{-1}$$

1 ni -1 ga bo'lish.

$$b^{2}-b=-\frac{26}{-1}$$

-26 ni -1 ga bo'lish.

$$b^{2}-b=26$$

-1 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{2} olish uchun. Keyin, -\frac{1}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$b^{2}-b+\left(-\frac{1}{2}\right)^{2}=26+\left(-\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$b^{2}-b+\frac{1}{4}=26+\frac{1}{4}$$

26 ni \frac{1}{4} ga qo'shish.

$$b^{2}-b+\frac{1}{4}=\frac{105}{4}$$

b^{2}-b+\frac{1}{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.

$$\left(b-\frac{1}{2}\right)^{2}=\frac{105}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(b-\frac{1}{2}\right)^{2}}=\sqrt{\frac{105}{4}}$$

Qisqartirish.

$$b-\frac{1}{2}=\frac{\sqrt{105}}{2} b-\frac{1}{2}=-\frac{\sqrt{105}}{2}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$b=\frac{\sqrt{105}+1}{2} b=\frac{1-\sqrt{105}}{2}$$