x^2+18x=7 eching

$$x ^ { 2 } + 18 x = 7$$

x uchun yechish

$$x=2\sqrt{22}-9\approx 0,38083152$$

$$x=-2\sqrt{22}-9\approx -18,38083152$$

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.

$$x^{2}+18x=7$$

Tenglamaning ikkala tarafidan 7 ni ayirish.

$$x^{2}+18x-7=7-7$$

O‘zidan 7 ayirilsa 0 qoladi.

$$x^{2}+18x-7=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 18 ni b va -7 ni c bilan almashtiring.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-7\right)}}{2}$$

18 kvadratini chiqarish.

$$x=\frac{-18±\sqrt{324-4\left(-7\right)}}{2}$$

-4 ni -7 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324+28}}{2}$$

324 ni 28 ga qo'shish.

$$x=\frac{-18±\sqrt{352}}{2}$$

352 ning kvadrat ildizini chiqarish.

$$x=\frac{-18±4\sqrt{22}}{2}$$

x=\frac{-18±4\sqrt{22}}{2} tenglamasini yeching, bunda ± musbat. -18 ni 4\sqrt{22} ga qo'shish.

$$x=\frac{4\sqrt{22}-18}{2}$$

-18+4\sqrt{22} ni 2 ga bo'lish.

$$x=2\sqrt{22}-9$$

x=\frac{-18±4\sqrt{22}}{2} tenglamasini yeching, bunda ± manfiy. -18 dan 4\sqrt{22} ni ayirish.

$$x=\frac{-4\sqrt{22}-18}{2}$$

-18-4\sqrt{22} ni 2 ga bo'lish.

$$x=-2\sqrt{22}-9$$

Tenglama yechildi.

$$x=2\sqrt{22}-9 x=-2\sqrt{22}-9$$

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.

$$x^{2}+18x=7$$

18 ni bo‘lish, x shartining koeffitsienti, 2 ga 9 olish uchun. Keyin, 9 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+18x+9^{2}=7+9^{2}$$

9 kvadratini chiqarish.

$$x^{2}+18x+81=7+81$$

7 ni 81 ga qo'shish.

$$x^{2}+18x+81=88$$

x^{2}+18x+81 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+9\right)^{2}=88$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{88}$$

Qisqartirish.

$$x+9=2\sqrt{22} x+9=-2\sqrt{22}$$

Tenglamaning ikkala tarafidan 9 ni ayirish.

$$x=2\sqrt{22}-9 x=-2\sqrt{22}-9$$