x^2-95x+2100=0 eching

$${ x }^{ 2 } -95x+2100=0$$

x uchun yechish

$$x=35$$

$$x=60$$

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.

$$x^{2}-95x+2100=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -95 ni b va 2100 ni c bilan almashtiring.

$$x=\frac{-\left(-95\right)±\sqrt{\left(-95\right)^{2}-4\times 2100}}{2}$$

-95 kvadratini chiqarish.

$$x=\frac{-\left(-95\right)±\sqrt{9025-4\times 2100}}{2}$$

-4 ni 2100 marotabaga ko'paytirish.

$$x=\frac{-\left(-95\right)±\sqrt{9025-8400}}{2}$$

9025 ni -8400 ga qo'shish.

$$x=\frac{-\left(-95\right)±\sqrt{625}}{2}$$

625 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-95\right)±25}{2}$$

-95 ning teskarisi 95 ga teng.

$$x=\frac{95±25}{2}$$

x=\frac{95±25}{2} tenglamasini yeching, bunda ± musbat. 95 ni 25 ga qo'shish.

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

120 ni 2 ga bo'lish.

$$x=60$$

x=\frac{95±25}{2} tenglamasini yeching, bunda ± manfiy. 95 dan 25 ni ayirish.

$$x=\frac{70}{2}$$

70 ni 2 ga bo'lish.

$$x=35$$

Tenglama yechildi.

$$x=60 x=35$$

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.

$$x^{2}-95x+2100=0$$

Tenglamaning ikkala tarafidan 2100 ni ayirish.

$$x^{2}-95x+2100-2100=-2100$$

O‘zidan 2100 ayirilsa 0 qoladi.

$$x^{2}-95x=-2100$$

-95 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{95}{2} olish uchun. Keyin, -\frac{95}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-95x+\left(-\frac{95}{2}\right)^{2}=-2100+\left(-\frac{95}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{95}{2} kvadratini chiqarish.

$$x^{2}-95x+\frac{9025}{4}=-2100+\frac{9025}{4}$$

-2100 ni \frac{9025}{4} ga qo'shish.

$$x^{2}-95x+\frac{9025}{4}=\frac{625}{4}$$

x^{2}-95x+\frac{9025}{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.

$$\left(x-\frac{95}{2}\right)^{2}=\frac{625}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{95}{2}\right)^{2}}=\sqrt{\frac{625}{4}}$$

Qisqartirish.

$$x-\frac{95}{2}=\frac{25}{2} x-\frac{95}{2}=-\frac{25}{2}$$

\frac{95}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=60 x=35$$