x^2=4x+20 eching

$$x ^ { 2 } = 4 x + 20$$

x uchun yechish

$$x=2\sqrt{6}+2\approx 6,898979486$$

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

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 4x ni ayirish.

$$x^{2}-4x=20$$

Ikkala tarafdan 20 ni ayirish.

$$x^{2}-4x-20=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -4 ni b va -20 ni c bilan almashtiring.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-20\right)}}{2}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-20\right)}}{2}$$

-4 ni -20 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+80}}{2}$$

16 ni 80 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{96}}{2}$$

96 ning kvadrat ildizini chiqarish.

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

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±4\sqrt{6}}{2}$$

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

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

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

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

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

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

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

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 4x ni ayirish.

$$x^{2}-4x=20$$

-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.

$$x^{2}-4x+\left(-2\right)^{2}=20+\left(-2\right)^{2}$$

-2 kvadratini chiqarish.

$$x^{2}-4x+4=20+4$$

20 ni 4 ga qo'shish.

$$x^{2}-4x+4=24$$

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

2 ni tenglamaning ikkala tarafiga qo'shish.

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