-x^2-2x+5=0 eching

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

x uchun yechish (complex solution)

$$x=\sqrt{6}-1\approx 1,449489743$$

$$x=-\left(\sqrt{6}+1\right)\approx -3,449489743$$

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.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -2 ni b va 5 ni c bilan almashtiring.

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

-2 kvadratini chiqarish.

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

-4 ni -1 marotabaga ko'paytirish.

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

4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+20}}{2\left(-1\right)}$$

4 ni 20 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{24}}{2\left(-1\right)}$$

24 ning kvadrat ildizini chiqarish.

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

-2 ning teskarisi 2 ga teng.

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

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{2±2\sqrt{6}}{-2}$$

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

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

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

$$x=-\left(\sqrt{6}+1\right)$$

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

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

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

$$x=\sqrt{6}-1$$

Tenglama yechildi.

$$x=-\left(\sqrt{6}+1\right) x=\sqrt{6}-1$$

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.

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

Tenglamaning ikkala tarafidan 5 ni ayirish.

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

O‘zidan 5 ayirilsa 0 qoladi.

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

Ikki tarafini -1 ga bo‘ling.

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

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

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

-2 ni -1 ga bo'lish.

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

-5 ni -1 ga bo'lish.

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

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

$$x^{2}+2x+1^{2}=5+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=5+1$$

5 ni 1 ga qo'shish.

$$x^{2}+2x+1=6$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{6}$$

Qisqartirish.

$$x+1=\sqrt{6} x+1=-\sqrt{6}$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=\sqrt{6}-1 x=-\sqrt{6}-1$$

x uchun yechish

$$x=\sqrt{6}-1\approx 1,449489743$$

$$x=-\sqrt{6}-1\approx -3,449489743$$

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.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -2 ni b va 5 ni c bilan almashtiring.

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

-2 kvadratini chiqarish.

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

-4 ni -1 marotabaga ko'paytirish.

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

4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+20}}{2\left(-1\right)}$$

4 ni 20 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{24}}{2\left(-1\right)}$$

24 ning kvadrat ildizini chiqarish.

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

-2 ning teskarisi 2 ga teng.

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

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{2±2\sqrt{6}}{-2}$$

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

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

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

$$x=-\left(\sqrt{6}+1\right)$$

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

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

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

$$x=\sqrt{6}-1$$

Tenglama yechildi.

$$x=-\left(\sqrt{6}+1\right) x=\sqrt{6}-1$$

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.

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

Tenglamaning ikkala tarafidan 5 ni ayirish.

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

O‘zidan 5 ayirilsa 0 qoladi.

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

Ikki tarafini -1 ga bo‘ling.

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

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

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

-2 ni -1 ga bo'lish.

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

-5 ni -1 ga bo'lish.

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

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

$$x^{2}+2x+1^{2}=5+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=5+1$$

5 ni 1 ga qo'shish.

$$x^{2}+2x+1=6$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{6}$$

Qisqartirish.

$$x+1=\sqrt{6} x+1=-\sqrt{6}$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=\sqrt{6}-1 x=-\sqrt{6}-1$$