2x^2+28x+148=0 eching

$$2 x ^ { 2 } + 28 x + 148 = 0$$

x uchun yechish (complex solution)

$$x=-7+5i$$

$$x=-7-5i$$

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.

$$2x^{2}+28x+148=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 28 ni b va 148 ni c bilan almashtiring.

$$x=\frac{-28±\sqrt{28^{2}-4\times 2\times 148}}{2\times 2}$$

28 kvadratini chiqarish.

$$x=\frac{-28±\sqrt{784-4\times 2\times 148}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-28±\sqrt{784-8\times 148}}{2\times 2}$$

-8 ni 148 marotabaga ko'paytirish.

$$x=\frac{-28±\sqrt{784-1184}}{2\times 2}$$

784 ni -1184 ga qo'shish.

$$x=\frac{-28±\sqrt{-400}}{2\times 2}$$

-400 ning kvadrat ildizini chiqarish.

$$x=\frac{-28±20i}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-28±20i}{4}$$

x=\frac{-28±20i}{4} tenglamasini yeching, bunda ± musbat. -28 ni 20i ga qo'shish.

$$x=\frac{-28+20i}{4}$$

-28+20i ni 4 ga bo'lish.

$$x=-7+5i$$

x=\frac{-28±20i}{4} tenglamasini yeching, bunda ± manfiy. -28 dan 20i ni ayirish.

$$x=\frac{-28-20i}{4}$$

-28-20i ni 4 ga bo'lish.

$$x=-7-5i$$

Tenglama yechildi.

$$x=-7+5i x=-7-5i$$

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.

$$2x^{2}+28x+148=0$$

Tenglamaning ikkala tarafidan 148 ni ayirish.

$$2x^{2}+28x+148-148=-148$$

O‘zidan 148 ayirilsa 0 qoladi.

$$2x^{2}+28x=-148$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+28x}{2}=-\frac{148}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{28}{2}x=-\frac{148}{2}$$

28 ni 2 ga bo'lish.

$$x^{2}+14x=-\frac{148}{2}$$

-148 ni 2 ga bo'lish.

$$x^{2}+14x=-74$$

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.

$$x^{2}+14x+7^{2}=-74+7^{2}$$

7 kvadratini chiqarish.

$$x^{2}+14x+49=-74+49$$

-74 ni 49 ga qo'shish.

$$x^{2}+14x+49=-25$$

x^{2}+14x+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.

$$\left(x+7\right)^{2}=-25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+7\right)^{2}}=\sqrt{-25}$$

Qisqartirish.

$$x+7=5i x+7=-5i$$

Tenglamaning ikkala tarafidan 7 ni ayirish.

$$x=-7+5i x=-7-5i$$