x^2+18x+12=0 eching

$$x ^ { 2 } + 18 x + 12 = 0$$

x uchun yechish (complex solution)

$$x=\sqrt{69}-9\approx -0,693376137$$

$$x=-\left(\sqrt{69}+9\right)\approx -17,306623863$$

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.

$$x^{2}+18x+12=0$$

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 12 ni c bilan almashtiring.

$$x=\frac{-18±\sqrt{18^{2}-4\times 12}}{2}$$

18 kvadratini chiqarish.

$$x=\frac{-18±\sqrt{324-4\times 12}}{2}$$

-4 ni 12 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324-48}}{2}$$

324 ni -48 ga qo'shish.

$$x=\frac{-18±\sqrt{276}}{2}$$

276 ning kvadrat ildizini chiqarish.

$$x=\frac{-18±2\sqrt{69}}{2}$$

x=\frac{-18±2\sqrt{69}}{2} tenglamasini yeching, bunda ± musbat. -18 ni 2\sqrt{69} ga qo'shish.

$$x=\frac{2\sqrt{69}-18}{2}$$

-18+2\sqrt{69} ni 2 ga bo'lish.

$$x=\sqrt{69}-9$$

x=\frac{-18±2\sqrt{69}}{2} tenglamasini yeching, bunda ± manfiy. -18 dan 2\sqrt{69} ni ayirish.

$$x=\frac{-2\sqrt{69}-18}{2}$$

-18-2\sqrt{69} ni 2 ga bo'lish.

$$x=-\sqrt{69}-9$$

Tenglama yechildi.

$$x=\sqrt{69}-9 x=-\sqrt{69}-9$$

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.

$$x^{2}+18x+12=0$$

Tenglamaning ikkala tarafidan 12 ni ayirish.

$$x^{2}+18x+12-12=-12$$

O‘zidan 12 ayirilsa 0 qoladi.

$$x^{2}+18x=-12$$

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.

$$x^{2}+18x+9^{2}=-12+9^{2}$$

9 kvadratini chiqarish.

$$x^{2}+18x+81=-12+81$$

-12 ni 81 ga qo'shish.

$$x^{2}+18x+81=69$$

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.

$$\left(x+9\right)^{2}=69$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{69}$$

Qisqartirish.

$$x+9=\sqrt{69} x+9=-\sqrt{69}$$

Tenglamaning ikkala tarafidan 9 ni ayirish.

$$x=\sqrt{69}-9 x=-\sqrt{69}-9$$

x uchun yechish

$$x=\sqrt{69}-9\approx -0,693376137$$

$$x=-\sqrt{69}-9\approx -17,306623863$$

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.

$$x^{2}+18x+12=0$$

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 12 ni c bilan almashtiring.

$$x=\frac{-18±\sqrt{18^{2}-4\times 12}}{2}$$

18 kvadratini chiqarish.

$$x=\frac{-18±\sqrt{324-4\times 12}}{2}$$

-4 ni 12 marotabaga ko'paytirish.

$$x=\frac{-18±\sqrt{324-48}}{2}$$

324 ni -48 ga qo'shish.

$$x=\frac{-18±\sqrt{276}}{2}$$

276 ning kvadrat ildizini chiqarish.

$$x=\frac{-18±2\sqrt{69}}{2}$$

x=\frac{-18±2\sqrt{69}}{2} tenglamasini yeching, bunda ± musbat. -18 ni 2\sqrt{69} ga qo'shish.

$$x=\frac{2\sqrt{69}-18}{2}$$

-18+2\sqrt{69} ni 2 ga bo'lish.

$$x=\sqrt{69}-9$$

x=\frac{-18±2\sqrt{69}}{2} tenglamasini yeching, bunda ± manfiy. -18 dan 2\sqrt{69} ni ayirish.

$$x=\frac{-2\sqrt{69}-18}{2}$$

-18-2\sqrt{69} ni 2 ga bo'lish.

$$x=-\sqrt{69}-9$$

Tenglama yechildi.

$$x=\sqrt{69}-9 x=-\sqrt{69}-9$$

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.

$$x^{2}+18x+12=0$$

Tenglamaning ikkala tarafidan 12 ni ayirish.

$$x^{2}+18x+12-12=-12$$

O‘zidan 12 ayirilsa 0 qoladi.

$$x^{2}+18x=-12$$

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.

$$x^{2}+18x+9^{2}=-12+9^{2}$$

9 kvadratini chiqarish.

$$x^{2}+18x+81=-12+81$$

-12 ni 81 ga qo'shish.

$$x^{2}+18x+81=69$$

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.

$$\left(x+9\right)^{2}=69$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{69}$$

Qisqartirish.

$$x+9=\sqrt{69} x+9=-\sqrt{69}$$

Tenglamaning ikkala tarafidan 9 ni ayirish.

$$x=\sqrt{69}-9 x=-\sqrt{69}-9$$