5-6x-x^2=0 eching

$$5 - 6 x - x ^ { 2 } = 0$$

x uchun yechish (complex solution)

$$x=\sqrt{14}-3\approx 0,741657387$$

$$x=-\left(\sqrt{14}+3\right)\approx -6,741657387$$

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.

$$-x^{2}-6x+5=0$$

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 5 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+4\times 5}}{2\left(-1\right)}$$

4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+20}}{2\left(-1\right)}$$

36 ni 20 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{56}}{2\left(-1\right)}$$

56 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±2\sqrt{14}}{2\left(-1\right)}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±2\sqrt{14}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{6±2\sqrt{14}}{-2}$$

x=\frac{6±2\sqrt{14}}{-2} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{14} ga qo'shish.

$$x=\frac{2\sqrt{14}+6}{-2}$$

6+2\sqrt{14} ni -2 ga bo'lish.

$$x=-\left(\sqrt{14}+3\right)$$

x=\frac{6±2\sqrt{14}}{-2} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{14} ni ayirish.

$$x=\frac{6-2\sqrt{14}}{-2}$$

6-2\sqrt{14} ni -2 ga bo'lish.

$$x=\sqrt{14}-3$$

Tenglama yechildi.

$$x=-\left(\sqrt{14}+3\right) x=\sqrt{14}-3$$

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.

$$-x^{2}-6x+5=0$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$-x^{2}-6x+5-5=-5$$

O‘zidan 5 ayirilsa 0 qoladi.

$$-x^{2}-6x=-5$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-6x}{-1}=-\frac{5}{-1}$$

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

$$x^{2}+\left(-\frac{6}{-1}\right)x=-\frac{5}{-1}$$

-6 ni -1 ga bo'lish.

$$x^{2}+6x=-\frac{5}{-1}$$

-5 ni -1 ga bo'lish.

$$x^{2}+6x=5$$

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.

$$x^{2}+6x+3^{2}=5+3^{2}$$

3 kvadratini chiqarish.

$$x^{2}+6x+9=5+9$$

5 ni 9 ga qo'shish.

$$x^{2}+6x+9=14$$

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.

$$\left(x+3\right)^{2}=14$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{14}$$

Qisqartirish.

$$x+3=\sqrt{14} x+3=-\sqrt{14}$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=\sqrt{14}-3 x=-\sqrt{14}-3$$

x uchun yechish

$$x=\sqrt{14}-3\approx 0,741657387$$

$$x=-\sqrt{14}-3\approx -6,741657387$$

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.

$$-x^{2}-6x+5=0$$

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 5 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+4\times 5}}{2\left(-1\right)}$$

4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+20}}{2\left(-1\right)}$$

36 ni 20 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{56}}{2\left(-1\right)}$$

56 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±2\sqrt{14}}{2\left(-1\right)}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±2\sqrt{14}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{6±2\sqrt{14}}{-2}$$

x=\frac{6±2\sqrt{14}}{-2} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{14} ga qo'shish.

$$x=\frac{2\sqrt{14}+6}{-2}$$

6+2\sqrt{14} ni -2 ga bo'lish.

$$x=-\left(\sqrt{14}+3\right)$$

x=\frac{6±2\sqrt{14}}{-2} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{14} ni ayirish.

$$x=\frac{6-2\sqrt{14}}{-2}$$

6-2\sqrt{14} ni -2 ga bo'lish.

$$x=\sqrt{14}-3$$

Tenglama yechildi.

$$x=-\left(\sqrt{14}+3\right) x=\sqrt{14}-3$$

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.

$$-x^{2}-6x+5=0$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$-x^{2}-6x+5-5=-5$$

O‘zidan 5 ayirilsa 0 qoladi.

$$-x^{2}-6x=-5$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-6x}{-1}=-\frac{5}{-1}$$

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

$$x^{2}+\left(-\frac{6}{-1}\right)x=-\frac{5}{-1}$$

-6 ni -1 ga bo'lish.

$$x^{2}+6x=-\frac{5}{-1}$$

-5 ni -1 ga bo'lish.

$$x^{2}+6x=5$$

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.

$$x^{2}+6x+3^{2}=5+3^{2}$$

3 kvadratini chiqarish.

$$x^{2}+6x+9=5+9$$

5 ni 9 ga qo'shish.

$$x^{2}+6x+9=14$$

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.

$$\left(x+3\right)^{2}=14$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{14}$$

Qisqartirish.

$$x+3=\sqrt{14} x+3=-\sqrt{14}$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=\sqrt{14}-3 x=-\sqrt{14}-3$$