x^2-120x+3600=0 eching

$${ x }^{ 2 } -120x+3600=0$$

x uchun yechish

$$x=60$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x^{2}-120x+3600=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -120 ni b va 3600 ni c bilan almashtiring.

$$x=\frac{-\left(-120\right)±\sqrt{\left(-120\right)^{2}-4\times 3600}}{2}$$

-120 kvadratini chiqarish.

$$x=\frac{-\left(-120\right)±\sqrt{14400-4\times 3600}}{2}$$

-4 ni 3600 marotabaga ko'paytirish.

$$x=\frac{-\left(-120\right)±\sqrt{14400-14400}}{2}$$

14400 ni -14400 ga qo'shish.

$$x=\frac{-\left(-120\right)±\sqrt{0}}{2}$$

0 ning kvadrat ildizini chiqarish.

$$x=-\frac{-120}{2}$$

-120 ning teskarisi 120 ga teng.

$$x=\frac{120}{2}$$

120 ni 2 ga bo'lish.

$$x=60$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}-120x+3600=0$$

x^{2}-120x+3600 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-60\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-60\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$x-60=0 x-60=0$$

60 ni tenglamaning ikkala tarafiga qo'shish.

$$x=60 x=60$$

Tenglama yechildi. Yechimlar bir xil.

$$x=60$$