x^2+134=-2x-14 eching

$${ x }^{ 2 } +134=-2x-14$$

x uchun yechish (complex solution)

$$x=-1+7\sqrt{3}i\approx -1+12,124355653i$$

$$x=-7\sqrt{3}i-1\approx -1-12,124355653i$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x ni ikki tarafga qo’shing.

$$x^{2}+134+2x=-14$$

14 ni ikki tarafga qo’shing.

$$x^{2}+134+2x+14=0$$

148 olish uchun 134 va 14'ni qo'shing.

$$x^{2}+148+2x=0$$

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.

$$x^{2}+2x+148=0$$

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 148 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}-4\times 148}}{2}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\times 148}}{2}$$

-4 ni 148 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4-592}}{2}$$

4 ni -592 ga qo'shish.

$$x=\frac{-2±\sqrt{-588}}{2}$$

-588 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±14\sqrt{3}i}{2}$$

x=\frac{-2±14\sqrt{3}i}{2} tenglamasini yeching, bunda ± musbat. -2 ni 14i\sqrt{3} ga qo'shish.

$$x=\frac{-2+14\sqrt{3}i}{2}$$

-2+14i\sqrt{3} ni 2 ga bo'lish.

$$x=-1+7\sqrt{3}i$$

x=\frac{-2±14\sqrt{3}i}{2} tenglamasini yeching, bunda ± manfiy. -2 dan 14i\sqrt{3} ni ayirish.

$$x=\frac{-14\sqrt{3}i-2}{2}$$

-2-14i\sqrt{3} ni 2 ga bo'lish.

$$x=-7\sqrt{3}i-1$$

Tenglama yechildi.

$$x=-1+7\sqrt{3}i x=-7\sqrt{3}i-1$$

Kvadratni yakunlash bo'yicha qadamlar

2x ni ikki tarafga qo’shing.

$$x^{2}+134+2x=-14$$

Ikkala tarafdan 134 ni ayirish.

$$x^{2}+2x=-14-134$$

-148 olish uchun -14 dan 134 ni ayirish.

$$x^{2}+2x=-148$$

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.

$$x^{2}+2x+1^{2}=-148+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=-148+1$$

-148 ni 1 ga qo'shish.

$$x^{2}+2x+1=-147$$

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.

$$\left(x+1\right)^{2}=-147$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{-147}$$

Qisqartirish.

$$x+1=7\sqrt{3}i x+1=-7\sqrt{3}i$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=-1+7\sqrt{3}i x=-7\sqrt{3}i-1$$