-375=(x+1)^2-4 eching

$$- 375 = ( x + 1 ) ^ { 2 } - 4$$

x uchun yechish (complex solution)

$$x=-\sqrt{371}i-1\approx -1-19,261360284i$$

$$x=-1+\sqrt{371}i\approx -1+19,261360284i$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+1\right)^{2} kengaytirilishi uchun ishlating.

$$-375=x^{2}+2x+1-4$$

-3 olish uchun 1 dan 4 ni ayirish.

$$-375=x^{2}+2x-3$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+2x-3=-375$$

375 ni ikki tarafga qo’shing.

$$x^{2}+2x-3+375=0$$

372 olish uchun -3 va 375'ni qo'shing.

$$x^{2}+2x+372=0$$

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 372 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}-4\times 372}}{2}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\times 372}}{2}$$

-4 ni 372 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4-1488}}{2}$$

4 ni -1488 ga qo'shish.

$$x=\frac{-2±\sqrt{-1484}}{2}$$

-1484 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{371}i}{2}$$

x=\frac{-2±2\sqrt{371}i}{2} tenglamasini yeching, bunda ± musbat. -2 ni 2i\sqrt{371} ga qo'shish.

$$x=\frac{-2+2\sqrt{371}i}{2}$$

-2+2i\sqrt{371} ni 2 ga bo'lish.

$$x=-1+\sqrt{371}i$$

x=\frac{-2±2\sqrt{371}i}{2} tenglamasini yeching, bunda ± manfiy. -2 dan 2i\sqrt{371} ni ayirish.

$$x=\frac{-2\sqrt{371}i-2}{2}$$

-2-2i\sqrt{371} ni 2 ga bo'lish.

$$x=-\sqrt{371}i-1$$

Tenglama yechildi.

$$x=-1+\sqrt{371}i x=-\sqrt{371}i-1$$

Kvadratni yakunlash bo'yicha qadamlar

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+1\right)^{2} kengaytirilishi uchun ishlating.

$$-375=x^{2}+2x+1-4$$

-3 olish uchun 1 dan 4 ni ayirish.

$$-375=x^{2}+2x-3$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+2x-3=-375$$

3 ni ikki tarafga qo’shing.

$$x^{2}+2x=-375+3$$

-372 olish uchun -375 va 3'ni qo'shing.

$$x^{2}+2x=-372$$

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.

$$x^{2}+2x+1^{2}=-372+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=-372+1$$

-372 ni 1 ga qo'shish.

$$x^{2}+2x+1=-371$$

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.

$$\left(x+1\right)^{2}=-371$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{-371}$$

Qisqartirish.

$$x+1=\sqrt{371}i x+1=-\sqrt{371}i$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=-1+\sqrt{371}i x=-\sqrt{371}i-1$$