w^2+14w+136=0 eching

$$w ^ { 2 } + 14 w + 136 = 0$$

w uchun yechish

$$w=-7+\sqrt{87}i\approx -7+9,327379053i$$

$$w=-\sqrt{87}i-7\approx -7-9,327379053i$$

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.

$$w^{2}+14w+136=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 14 ni b va 136 ni c bilan almashtiring.

$$w=\frac{-14±\sqrt{14^{2}-4\times 136}}{2}$$

14 kvadratini chiqarish.

$$w=\frac{-14±\sqrt{196-4\times 136}}{2}$$

-4 ni 136 marotabaga ko'paytirish.

$$w=\frac{-14±\sqrt{196-544}}{2}$$

196 ni -544 ga qo'shish.

$$w=\frac{-14±\sqrt{-348}}{2}$$

-348 ning kvadrat ildizini chiqarish.

$$w=\frac{-14±2\sqrt{87}i}{2}$$

w=\frac{-14±2\sqrt{87}i}{2} tenglamasini yeching, bunda ± musbat. -14 ni 2i\sqrt{87} ga qo'shish.

$$w=\frac{-14+2\sqrt{87}i}{2}$$

-14+2i\sqrt{87} ni 2 ga bo'lish.

$$w=-7+\sqrt{87}i$$

w=\frac{-14±2\sqrt{87}i}{2} tenglamasini yeching, bunda ± manfiy. -14 dan 2i\sqrt{87} ni ayirish.

$$w=\frac{-2\sqrt{87}i-14}{2}$$

-14-2i\sqrt{87} ni 2 ga bo'lish.

$$w=-\sqrt{87}i-7$$

Tenglama yechildi.

$$w=-7+\sqrt{87}i w=-\sqrt{87}i-7$$

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.

$$w^{2}+14w+136=0$$

Tenglamaning ikkala tarafidan 136 ni ayirish.

$$w^{2}+14w+136-136=-136$$

O‘zidan 136 ayirilsa 0 qoladi.

$$w^{2}+14w=-136$$

14 ni bo‘lish, x shartining koeffitsienti, 2 ga 7 olish uchun. Keyin, 7 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$w^{2}+14w+7^{2}=-136+7^{2}$$

7 kvadratini chiqarish.

$$w^{2}+14w+49=-136+49$$

-136 ni 49 ga qo'shish.

$$w^{2}+14w+49=-87$$

w^{2}+14w+49 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(w+7\right)^{2}=-87$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(w+7\right)^{2}}=\sqrt{-87}$$

Qisqartirish.

$$w+7=\sqrt{87}i w+7=-\sqrt{87}i$$

Tenglamaning ikkala tarafidan 7 ni ayirish.

$$w=-7+\sqrt{87}i w=-\sqrt{87}i-7$$