-x^2-8x+12=0 eching

$$- x ^ { 2 } - 8 x + 12 = 0$$

x uchun yechish

$$x=2\sqrt{7}-4\approx 1,291502622$$

$$x=-2\sqrt{7}-4\approx -9,291502622$$

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.

$$-x^{2}-8x+12=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -8 ni b va 12 ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-1\right)\times 12}}{2\left(-1\right)}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-1\right)\times 12}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+4\times 12}}{2\left(-1\right)}$$

4 ni 12 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+48}}{2\left(-1\right)}$$

64 ni 48 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{112}}{2\left(-1\right)}$$

112 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±4\sqrt{7}}{2\left(-1\right)}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±4\sqrt{7}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{8±4\sqrt{7}}{-2}$$

x=\frac{8±4\sqrt{7}}{-2} tenglamasini yeching, bunda ± musbat. 8 ni 4\sqrt{7} ga qo'shish.

$$x=\frac{4\sqrt{7}+8}{-2}$$

8+4\sqrt{7} ni -2 ga bo'lish.

$$x=-2\sqrt{7}-4$$

x=\frac{8±4\sqrt{7}}{-2} tenglamasini yeching, bunda ± manfiy. 8 dan 4\sqrt{7} ni ayirish.

$$x=\frac{8-4\sqrt{7}}{-2}$$

8-4\sqrt{7} ni -2 ga bo'lish.

$$x=2\sqrt{7}-4$$

Tenglama yechildi.

$$x=-2\sqrt{7}-4 x=2\sqrt{7}-4$$

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.

$$-x^{2}-8x+12=0$$

Tenglamaning ikkala tarafidan 12 ni ayirish.

$$-x^{2}-8x+12-12=-12$$

O‘zidan 12 ayirilsa 0 qoladi.

$$-x^{2}-8x=-12$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-8x}{-1}=-\frac{12}{-1}$$

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

$$x^{2}+\left(-\frac{8}{-1}\right)x=-\frac{12}{-1}$$

-8 ni -1 ga bo'lish.

$$x^{2}+8x=-\frac{12}{-1}$$

-12 ni -1 ga bo'lish.

$$x^{2}+8x=12$$

8 ni bo‘lish, x shartining koeffitsienti, 2 ga 4 olish uchun. Keyin, 4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+8x+4^{2}=12+4^{2}$$

4 kvadratini chiqarish.

$$x^{2}+8x+16=12+16$$

12 ni 16 ga qo'shish.

$$x^{2}+8x+16=28$$

x^{2}+8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+4\right)^{2}=28$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{28}$$

Qisqartirish.

$$x+4=2\sqrt{7} x+4=-2\sqrt{7}$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x=2\sqrt{7}-4 x=-2\sqrt{7}-4$$