6x^2+12x+14=7x^2-5 eching

$$6 x ^ { 2 } + 12 x + 14 = 7 x ^ { 2 } - 5$$

x uchun yechish

$$x=\sqrt{55}+6\approx 13,416198487$$

$$x=6-\sqrt{55}\approx -1,416198487$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 7x^{2} ni ayirish.

$$6x^{2}+12x+14-7x^{2}=-5$$

-x^{2} ni olish uchun 6x^{2} va -7x^{2} ni birlashtirish.

$$-x^{2}+12x+14=-5$$

5 ni ikki tarafga qo’shing.

$$-x^{2}+12x+14+5=0$$

19 olish uchun 14 va 5'ni qo'shing.

$$-x^{2}+12x+19=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 12 ni b va 19 ni c bilan almashtiring.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-1\right)\times 19}}{2\left(-1\right)}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\left(-1\right)\times 19}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+4\times 19}}{2\left(-1\right)}$$

4 ni 19 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+76}}{2\left(-1\right)}$$

144 ni 76 ga qo'shish.

$$x=\frac{-12±\sqrt{220}}{2\left(-1\right)}$$

220 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±2\sqrt{55}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-12±2\sqrt{55}}{-2}$$

x=\frac{-12±2\sqrt{55}}{-2} tenglamasini yeching, bunda ± musbat. -12 ni 2\sqrt{55} ga qo'shish.

$$x=\frac{2\sqrt{55}-12}{-2}$$

-12+2\sqrt{55} ni -2 ga bo'lish.

$$x=6-\sqrt{55}$$

x=\frac{-12±2\sqrt{55}}{-2} tenglamasini yeching, bunda ± manfiy. -12 dan 2\sqrt{55} ni ayirish.

$$x=\frac{-2\sqrt{55}-12}{-2}$$

-12-2\sqrt{55} ni -2 ga bo'lish.

$$x=\sqrt{55}+6$$

Tenglama yechildi.

$$x=6-\sqrt{55} x=\sqrt{55}+6$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 7x^{2} ni ayirish.

$$6x^{2}+12x+14-7x^{2}=-5$$

-x^{2} ni olish uchun 6x^{2} va -7x^{2} ni birlashtirish.

$$-x^{2}+12x+14=-5$$

Ikkala tarafdan 14 ni ayirish.

$$-x^{2}+12x=-5-14$$

-19 olish uchun -5 dan 14 ni ayirish.

$$-x^{2}+12x=-19$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+12x}{-1}=-\frac{19}{-1}$$

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

$$x^{2}+\frac{12}{-1}x=-\frac{19}{-1}$$

12 ni -1 ga bo'lish.

$$x^{2}-12x=-\frac{19}{-1}$$

-19 ni -1 ga bo'lish.

$$x^{2}-12x=19$$

-12 ni bo‘lish, x shartining koeffitsienti, 2 ga -6 olish uchun. Keyin, -6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-12x+\left(-6\right)^{2}=19+\left(-6\right)^{2}$$

-6 kvadratini chiqarish.

$$x^{2}-12x+36=19+36$$

19 ni 36 ga qo'shish.

$$x^{2}-12x+36=55$$

x^{2}-12x+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-6\right)^{2}=55$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{55}$$

Qisqartirish.

$$x-6=\sqrt{55} x-6=-\sqrt{55}$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{55}+6 x=6-\sqrt{55}$$