x^2-76x=-68 eching

$$x ^ { 2 } - 76 x = - 68$$

x uchun yechish

$$x=4\sqrt{86}+38\approx 75,094473982$$

$$x=38-4\sqrt{86}\approx 0,905526018$$

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.

$$x^{2}-76x=-68$$

68 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-76x-\left(-68\right)=-68-\left(-68\right)$$

O‘zidan -68 ayirilsa 0 qoladi.

$$x^{2}-76x-\left(-68\right)=0$$

0 dan -68 ni ayirish.

$$x^{2}-76x+68=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -76 ni b va 68 ni c bilan almashtiring.

$$x=\frac{-\left(-76\right)±\sqrt{\left(-76\right)^{2}-4\times 68}}{2}$$

-76 kvadratini chiqarish.

$$x=\frac{-\left(-76\right)±\sqrt{5776-4\times 68}}{2}$$

-4 ni 68 marotabaga ko'paytirish.

$$x=\frac{-\left(-76\right)±\sqrt{5776-272}}{2}$$

5776 ni -272 ga qo'shish.

$$x=\frac{-\left(-76\right)±\sqrt{5504}}{2}$$

5504 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-76\right)±8\sqrt{86}}{2}$$

-76 ning teskarisi 76 ga teng.

$$x=\frac{76±8\sqrt{86}}{2}$$

x=\frac{76±8\sqrt{86}}{2} tenglamasini yeching, bunda ± musbat. 76 ni 8\sqrt{86} ga qo'shish.

$$x=\frac{8\sqrt{86}+76}{2}$$

76+8\sqrt{86} ni 2 ga bo'lish.

$$x=4\sqrt{86}+38$$

x=\frac{76±8\sqrt{86}}{2} tenglamasini yeching, bunda ± manfiy. 76 dan 8\sqrt{86} ni ayirish.

$$x=\frac{76-8\sqrt{86}}{2}$$

76-8\sqrt{86} ni 2 ga bo'lish.

$$x=38-4\sqrt{86}$$

Tenglama yechildi.

$$x=4\sqrt{86}+38 x=38-4\sqrt{86}$$

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.

$$x^{2}-76x=-68$$

-76 ni bo‘lish, x shartining koeffitsienti, 2 ga -38 olish uchun. Keyin, -38 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-76x+\left(-38\right)^{2}=-68+\left(-38\right)^{2}$$

-38 kvadratini chiqarish.

$$x^{2}-76x+1444=-68+1444$$

-68 ni 1444 ga qo'shish.

$$x^{2}-76x+1444=1376$$

x^{2}-76x+1444 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-38\right)^{2}=1376$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-38\right)^{2}}=\sqrt{1376}$$

Qisqartirish.

$$x-38=4\sqrt{86} x-38=-4\sqrt{86}$$

38 ni tenglamaning ikkala tarafiga qo'shish.

$$x=4\sqrt{86}+38 x=38-4\sqrt{86}$$