2x(x+4)=1 eching

$$2 x ( x + 4 ) = 1$$

x uchun yechish

$$x=\frac{3\sqrt{2}}{2}-2\approx 0,121320344$$

$$x=-\frac{3\sqrt{2}}{2}-2\approx -4,121320344$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+8x=1$$

Ikkala tarafdan 1 ni ayirish.

$$2x^{2}+8x-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 8 ni b va -1 ni c bilan almashtiring.

$$x=\frac{-8±\sqrt{8^{2}-4\times 2\left(-1\right)}}{2\times 2}$$

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\times 2\left(-1\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64-8\left(-1\right)}}{2\times 2}$$

-8 ni -1 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+8}}{2\times 2}$$

64 ni 8 ga qo'shish.

$$x=\frac{-8±\sqrt{72}}{2\times 2}$$

72 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±6\sqrt{2}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-8±6\sqrt{2}}{4}$$

x=\frac{-8±6\sqrt{2}}{4} tenglamasini yeching, bunda ± musbat. -8 ni 6\sqrt{2} ga qo'shish.

$$x=\frac{6\sqrt{2}-8}{4}$$

-8+6\sqrt{2} ni 4 ga bo'lish.

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

x=\frac{-8±6\sqrt{2}}{4} tenglamasini yeching, bunda ± manfiy. -8 dan 6\sqrt{2} ni ayirish.

$$x=\frac{-6\sqrt{2}-8}{4}$$

-8-6\sqrt{2} ni 4 ga bo'lish.

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

2x ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+8x=1$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+8x}{2}=\frac{1}{2}$$

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

$$x^{2}+\frac{8}{2}x=\frac{1}{2}$$

8 ni 2 ga bo'lish.

$$x^{2}+4x=\frac{1}{2}$$

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

$$x^{2}+4x+2^{2}=\frac{1}{2}+2^{2}$$

2 kvadratini chiqarish.

$$x^{2}+4x+4=\frac{1}{2}+4$$

\frac{1}{2} ni 4 ga qo'shish.

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

x^{2}+4x+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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

Tenglamaning ikkala tarafidan 2 ni ayirish.

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