-left(x+3right)^2-4(3x+1)=0 eching

$$- { \left(x+3 \right) }^{ 2 } -4(3x+1)=0$$

x uchun yechish

$$x=2\sqrt{17}-9\approx -0,753788749$$

$$x=-2\sqrt{17}-9\approx -17,246211251$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+3\right)^{2} kengaytirilishi uchun ishlating.

$$-\left(x^{2}+6x+9\right)-4\left(3x+1\right)=0$$

x^{2}+6x+9 teskarisini topish uchun har birining teskarisini toping.

$$-x^{2}-6x-9-4\left(3x+1\right)=0$$

-4 ga 3x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-x^{2}-6x-9-12x-4=0$$

-18x ni olish uchun -6x va -12x ni birlashtirish.

$$-x^{2}-18x-9-4=0$$

-13 olish uchun -9 dan 4 ni ayirish.

$$-x^{2}-18x-13=0$$

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 -13 ni c bilan almashtiring.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\left(-1\right)\left(-13\right)}}{2\left(-1\right)}$$

-18 kvadratini chiqarish.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\left(-1\right)\left(-13\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324+4\left(-13\right)}}{2\left(-1\right)}$$

4 ni -13 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324-52}}{2\left(-1\right)}$$

324 ni -52 ga qo'shish.

$$x=\frac{-\left(-18\right)±\sqrt{272}}{2\left(-1\right)}$$

272 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-18\right)±4\sqrt{17}}{2\left(-1\right)}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±4\sqrt{17}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{18±4\sqrt{17}}{-2}$$

x=\frac{18±4\sqrt{17}}{-2} tenglamasini yeching, bunda ± musbat. 18 ni 4\sqrt{17} ga qo'shish.

$$x=\frac{4\sqrt{17}+18}{-2}$$

18+4\sqrt{17} ni -2 ga bo'lish.

$$x=-2\sqrt{17}-9$$

x=\frac{18±4\sqrt{17}}{-2} tenglamasini yeching, bunda ± manfiy. 18 dan 4\sqrt{17} ni ayirish.

$$x=\frac{18-4\sqrt{17}}{-2}$$

18-4\sqrt{17} ni -2 ga bo'lish.

$$x=2\sqrt{17}-9$$

Tenglama yechildi.

$$x=-2\sqrt{17}-9 x=2\sqrt{17}-9$$

Kvadratni yakunlash bo'yicha qadamlar

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+3\right)^{2} kengaytirilishi uchun ishlating.

$$-\left(x^{2}+6x+9\right)-4\left(3x+1\right)=0$$

x^{2}+6x+9 teskarisini topish uchun har birining teskarisini toping.

$$-x^{2}-6x-9-4\left(3x+1\right)=0$$

-4 ga 3x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-x^{2}-6x-9-12x-4=0$$

-18x ni olish uchun -6x va -12x ni birlashtirish.

$$-x^{2}-18x-9-4=0$$

-13 olish uchun -9 dan 4 ni ayirish.

$$-x^{2}-18x-13=0$$

13 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$-x^{2}-18x=13$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-18x}{-1}=\frac{13}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{18}{-1}\right)x=\frac{13}{-1}$$

-18 ni -1 ga bo'lish.

$$x^{2}+18x=\frac{13}{-1}$$

13 ni -1 ga bo'lish.

$$x^{2}+18x=-13$$

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.

$$x^{2}+18x+9^{2}=-13+9^{2}$$

9 kvadratini chiqarish.

$$x^{2}+18x+81=-13+81$$

-13 ni 81 ga qo'shish.

$$x^{2}+18x+81=68$$

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.

$$\left(x+9\right)^{2}=68$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+9\right)^{2}}=\sqrt{68}$$

Qisqartirish.

$$x+9=2\sqrt{17} x+9=-2\sqrt{17}$$

Tenglamaning ikkala tarafidan 9 ni ayirish.

$$x=2\sqrt{17}-9 x=-2\sqrt{17}-9$$