20^2=x(x-6) eching

$${ 20 }^{ 2 } =x(x-6)$$

x uchun yechish

$$x=\sqrt{409}+3\approx 23,223748416$$

$$x=3-\sqrt{409}\approx -17,223748416$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 daraja ko‘rsatkichini 20 ga hisoblang va 400 ni qiymatni oling.

$$400=x\left(x-6\right)$$

x ga x-6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$400=x^{2}-6x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-6x=400$$

Ikkala tarafdan 400 ni ayirish.

$$x^{2}-6x-400=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -6 ni b va -400 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-400\right)}}{2}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-400\right)}}{2}$$

-4 ni -400 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+1600}}{2}$$

36 ni 1600 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{1636}}{2}$$

1636 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±2\sqrt{409}}{2}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±2\sqrt{409}}{2}$$

x=\frac{6±2\sqrt{409}}{2} tenglamasini yeching, bunda ± musbat. 6 ni 2\sqrt{409} ga qo'shish.

$$x=\frac{2\sqrt{409}+6}{2}$$

6+2\sqrt{409} ni 2 ga bo'lish.

$$x=\sqrt{409}+3$$

x=\frac{6±2\sqrt{409}}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 2\sqrt{409} ni ayirish.

$$x=\frac{6-2\sqrt{409}}{2}$$

6-2\sqrt{409} ni 2 ga bo'lish.

$$x=3-\sqrt{409}$$

Tenglama yechildi.

$$x=\sqrt{409}+3 x=3-\sqrt{409}$$

Kvadratni yakunlash bo'yicha qadamlar

2 daraja ko‘rsatkichini 20 ga hisoblang va 400 ni qiymatni oling.

$$400=x\left(x-6\right)$$

x ga x-6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$400=x^{2}-6x$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-6x=400$$

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-6x+\left(-3\right)^{2}=400+\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

$$x^{2}-6x+9=400+9$$

400 ni 9 ga qo'shish.

$$x^{2}-6x+9=409$$

x^{2}-6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-3\right)^{2}=409$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{409}$$

Qisqartirish.

$$x-3=\sqrt{409} x-3=-\sqrt{409}$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{409}+3 x=3-\sqrt{409}$$