4=(x-300)(x-300) eching

$$4=(x-300)(x-300)$$

x uchun yechish

$$x=302$$

$$x=298$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(x-300\right)^{2} hosil qilish uchun x-300 va x-300 ni ko'paytirish.

$$4=\left(x-300\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-300\right)^{2} kengaytirilishi uchun ishlating.

$$4=x^{2}-600x+90000$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-600x+90000=4$$

Ikkala tarafdan 4 ni ayirish.

$$x^{2}-600x+90000-4=0$$

89996 olish uchun 90000 dan 4 ni ayirish.

$$x^{2}-600x+89996=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -600 ni b va 89996 ni c bilan almashtiring.

$$x=\frac{-\left(-600\right)±\sqrt{\left(-600\right)^{2}-4\times 89996}}{2}$$

-600 kvadratini chiqarish.

$$x=\frac{-\left(-600\right)±\sqrt{360000-4\times 89996}}{2}$$

-4 ni 89996 marotabaga ko'paytirish.

$$x=\frac{-\left(-600\right)±\sqrt{360000-359984}}{2}$$

360000 ni -359984 ga qo'shish.

$$x=\frac{-\left(-600\right)±\sqrt{16}}{2}$$

16 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-600\right)±4}{2}$$

-600 ning teskarisi 600 ga teng.

$$x=\frac{600±4}{2}$$

x=\frac{600±4}{2} tenglamasini yeching, bunda ± musbat. 600 ni 4 ga qo'shish.

$$x=\frac{604}{2}$$

604 ni 2 ga bo'lish.

$$x=302$$

x=\frac{600±4}{2} tenglamasini yeching, bunda ± manfiy. 600 dan 4 ni ayirish.

$$x=\frac{596}{2}$$

596 ni 2 ga bo'lish.

$$x=298$$

Tenglama yechildi.

$$x=302 x=298$$

Kvadratni yakunlash bo'yicha qadamlar

\left(x-300\right)^{2} hosil qilish uchun x-300 va x-300 ni ko'paytirish.

$$4=\left(x-300\right)^{2}$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-300\right)^{2} kengaytirilishi uchun ishlating.

$$4=x^{2}-600x+90000$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}-600x+90000=4$$

x^{2}-600x+90000 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-300\right)^{2}=4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-300\right)^{2}}=\sqrt{4}$$

Qisqartirish.

$$x-300=2 x-300=-2$$

300 ni tenglamaning ikkala tarafiga qo'shish.

$$x=302 x=298$$