2x^2+10x+1=x^2 eching

$$2 x ^ { 2 } + 10 x + 1 = x ^ { 2 }$$

x uchun yechish

$$x=2\sqrt{6}-5\approx -0,101020514$$

$$x=-2\sqrt{6}-5\approx -9,898979486$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan x^{2} ni ayirish.

$$2x^{2}+10x+1-x^{2}=0$$

x^{2} ni olish uchun 2x^{2} va -x^{2} ni birlashtirish.

$$x^{2}+10x+1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 10 ni b va 1 ni c bilan almashtiring.

$$x=\frac{-10±\sqrt{10^{2}-4}}{2}$$

10 kvadratini chiqarish.

$$x=\frac{-10±\sqrt{100-4}}{2}$$

100 ni -4 ga qo'shish.

$$x=\frac{-10±\sqrt{96}}{2}$$

96 ning kvadrat ildizini chiqarish.

$$x=\frac{-10±4\sqrt{6}}{2}$$

x=\frac{-10±4\sqrt{6}}{2} tenglamasini yeching, bunda ± musbat. -10 ni 4\sqrt{6} ga qo'shish.

$$x=\frac{4\sqrt{6}-10}{2}$$

-10+4\sqrt{6} ni 2 ga bo'lish.

$$x=2\sqrt{6}-5$$

x=\frac{-10±4\sqrt{6}}{2} tenglamasini yeching, bunda ± manfiy. -10 dan 4\sqrt{6} ni ayirish.

$$x=\frac{-4\sqrt{6}-10}{2}$$

-10-4\sqrt{6} ni 2 ga bo'lish.

$$x=-2\sqrt{6}-5$$

Tenglama yechildi.

$$x=2\sqrt{6}-5 x=-2\sqrt{6}-5$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan x^{2} ni ayirish.

$$2x^{2}+10x+1-x^{2}=0$$

x^{2} ni olish uchun 2x^{2} va -x^{2} ni birlashtirish.

$$x^{2}+10x+1=0$$

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}+10x=-1$$

10 ni bo‘lish, x shartining koeffitsienti, 2 ga 5 olish uchun. Keyin, 5 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+10x+5^{2}=-1+5^{2}$$

5 kvadratini chiqarish.

$$x^{2}+10x+25=-1+25$$

-1 ni 25 ga qo'shish.

$$x^{2}+10x+25=24$$

x^{2}+10x+25 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+5\right)^{2}=24$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{24}$$

Qisqartirish.

$$x+5=2\sqrt{6} x+5=-2\sqrt{6}$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$x=2\sqrt{6}-5 x=-2\sqrt{6}-5$$