3=-2x^2-6x eching

$$3 = - 2 x ^ { 2 } - 6 x$$

x uchun yechish

$$x=\frac{\sqrt{3}-3}{2}\approx -0,633974596$$

$$x=\frac{-\sqrt{3}-3}{2}\approx -2,366025404$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-2x^{2}-6x=3$$

Ikkala tarafdan 3 ni ayirish.

$$-2x^{2}-6x-3=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, -6 ni b va -3 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-2\right)\left(-3\right)}}{2\left(-2\right)}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-2\right)\left(-3\right)}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+8\left(-3\right)}}{2\left(-2\right)}$$

8 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36-24}}{2\left(-2\right)}$$

36 ni -24 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{12}}{2\left(-2\right)}$$

12 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±2\sqrt{3}}{2\left(-2\right)}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±2\sqrt{3}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{6±2\sqrt{3}}{-4}$$

x=\frac{6±2\sqrt{3}}{-4} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{3} ga qo'shish.

$$x=\frac{2\sqrt{3}+6}{-4}$$

6+2\sqrt{3} ni -4 ga bo'lish.

$$x=\frac{-\sqrt{3}-3}{2}$$

x=\frac{6±2\sqrt{3}}{-4} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{3} ni ayirish.

$$x=\frac{6-2\sqrt{3}}{-4}$$

6-2\sqrt{3} ni -4 ga bo'lish.

$$x=\frac{\sqrt{3}-3}{2}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{3}-3}{2} x=\frac{\sqrt{3}-3}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-2x^{2}-6x=3$$

Ikki tarafini -2 ga bo‘ling.

$$\frac{-2x^{2}-6x}{-2}=\frac{3}{-2}$$

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

$$x^{2}+\left(-\frac{6}{-2}\right)x=\frac{3}{-2}$$

-6 ni -2 ga bo'lish.

$$x^{2}+3x=\frac{3}{-2}$$

3 ni -2 ga bo'lish.

$$x^{2}+3x=-\frac{3}{2}$$

3 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{2} olish uchun. Keyin, \frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=-\frac{3}{2}+\left(\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{2} kvadratini chiqarish.

$$x^{2}+3x+\frac{9}{4}=-\frac{3}{2}+\frac{9}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{3}{2} ni \frac{9}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+3x+\frac{9}{4}=\frac{3}{4}$$

x^{2}+3x+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{3}{2}\right)^{2}=\frac{3}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{3}{4}}$$

Qisqartirish.

$$x+\frac{3}{2}=\frac{\sqrt{3}}{2} x+\frac{3}{2}=-\frac{\sqrt{3}}{2}$$

Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.

$$x=\frac{\sqrt{3}-3}{2} x=\frac{-\sqrt{3}-3}{2}$$