x^2+2584=106x eching

$${ x }^{ 2 } +2584=106x$$

x uchun yechish

$$x=38$$

$$x=68$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 106x ni ayirish.

$$x^{2}+2584-106x=0$$

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.

$$x^{2}-106x+2584=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -106 ni b va 2584 ni c bilan almashtiring.

$$x=\frac{-\left(-106\right)±\sqrt{\left(-106\right)^{2}-4\times 2584}}{2}$$

-106 kvadratini chiqarish.

$$x=\frac{-\left(-106\right)±\sqrt{11236-4\times 2584}}{2}$$

-4 ni 2584 marotabaga ko'paytirish.

$$x=\frac{-\left(-106\right)±\sqrt{11236-10336}}{2}$$

11236 ni -10336 ga qo'shish.

$$x=\frac{-\left(-106\right)±\sqrt{900}}{2}$$

900 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-106\right)±30}{2}$$

-106 ning teskarisi 106 ga teng.

$$x=\frac{106±30}{2}$$

x=\frac{106±30}{2} tenglamasini yeching, bunda ± musbat. 106 ni 30 ga qo'shish.

$$x=\frac{136}{2}$$

136 ni 2 ga bo'lish.

$$x=68$$

x=\frac{106±30}{2} tenglamasini yeching, bunda ± manfiy. 106 dan 30 ni ayirish.

$$x=\frac{76}{2}$$

76 ni 2 ga bo'lish.

$$x=38$$

Tenglama yechildi.

$$x=68 x=38$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 106x ni ayirish.

$$x^{2}+2584-106x=0$$

Ikkala tarafdan 2584 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-106x=-2584$$

-106 ni bo‘lish, x shartining koeffitsienti, 2 ga -53 olish uchun. Keyin, -53 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-106x+\left(-53\right)^{2}=-2584+\left(-53\right)^{2}$$

-53 kvadratini chiqarish.

$$x^{2}-106x+2809=-2584+2809$$

-2584 ni 2809 ga qo'shish.

$$x^{2}-106x+2809=225$$

x^{2}-106x+2809 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-53\right)^{2}=225$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-53\right)^{2}}=\sqrt{225}$$

Qisqartirish.

$$x-53=15 x-53=-15$$

53 ni tenglamaning ikkala tarafiga qo'shish.

$$x=68 x=38$$