-x^2-6x+35=0 eching

$$- { x }^{ 2 } -6x+35=0$$

x uchun yechish

$$x=2\sqrt{11}-3\approx 3,633249581$$

$$x=-2\sqrt{11}-3\approx -9,633249581$$

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.

$$-x^{2}-6x+35=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -6 ni b va 35 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-1\right)\times 35}}{2\left(-1\right)}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-1\right)\times 35}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+4\times 35}}{2\left(-1\right)}$$

4 ni 35 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+140}}{2\left(-1\right)}$$

36 ni 140 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{176}}{2\left(-1\right)}$$

176 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±4\sqrt{11}}{2\left(-1\right)}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±4\sqrt{11}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{6±4\sqrt{11}}{-2}$$

x=\frac{6±4\sqrt{11}}{-2} tenglamasini yeching, bunda ± musbat. 6 ni 4\sqrt{11} ga qo'shish.

$$x=\frac{4\sqrt{11}+6}{-2}$$

6+4\sqrt{11} ni -2 ga bo'lish.

$$x=-2\sqrt{11}-3$$

x=\frac{6±4\sqrt{11}}{-2} tenglamasini yeching, bunda ± manfiy. 6 dan 4\sqrt{11} ni ayirish.

$$x=\frac{6-4\sqrt{11}}{-2}$$

6-4\sqrt{11} ni -2 ga bo'lish.

$$x=2\sqrt{11}-3$$

Tenglama yechildi.

$$x=-2\sqrt{11}-3 x=2\sqrt{11}-3$$

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.

$$-x^{2}-6x+35=0$$

Tenglamaning ikkala tarafidan 35 ni ayirish.

$$-x^{2}-6x+35-35=-35$$

O‘zidan 35 ayirilsa 0 qoladi.

$$-x^{2}-6x=-35$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-6x}{-1}=-\frac{35}{-1}$$

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

$$x^{2}+\left(-\frac{6}{-1}\right)x=-\frac{35}{-1}$$

-6 ni -1 ga bo'lish.

$$x^{2}+6x=-\frac{35}{-1}$$

-35 ni -1 ga bo'lish.

$$x^{2}+6x=35$$

6 ni bo‘lish, x shartining koeffitsienti, 2 ga 3 olish uchun. Keyin, 3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+6x+3^{2}=35+3^{2}$$

3 kvadratini chiqarish.

$$x^{2}+6x+9=35+9$$

35 ni 9 ga qo'shish.

$$x^{2}+6x+9=44$$

x^{2}+6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+3\right)^{2}=44$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{44}$$

Qisqartirish.

$$x+3=2\sqrt{11} x+3=-2\sqrt{11}$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=2\sqrt{11}-3 x=-2\sqrt{11}-3$$