76x-76=x^2+8x eching

$$76 x - 76 = x ^ { 2 } + 8 x$$

x uchun yechish

$$x=6\sqrt{30}+34\approx 66,86335345$$

$$x=34-6\sqrt{30}\approx 1,13664655$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan x^{2} ni ayirish.

$$76x-76-x^{2}=8x$$

Ikkala tarafdan 8x ni ayirish.

$$76x-76-x^{2}-8x=0$$

68x ni olish uchun 76x va -8x ni birlashtirish.

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

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.

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

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

$$x=\frac{-68±\sqrt{68^{2}-4\left(-1\right)\left(-76\right)}}{2\left(-1\right)}$$

68 kvadratini chiqarish.

$$x=\frac{-68±\sqrt{4624-4\left(-1\right)\left(-76\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-68±\sqrt{4624+4\left(-76\right)}}{2\left(-1\right)}$$

4 ni -76 marotabaga ko'paytirish.

$$x=\frac{-68±\sqrt{4624-304}}{2\left(-1\right)}$$

4624 ni -304 ga qo'shish.

$$x=\frac{-68±\sqrt{4320}}{2\left(-1\right)}$$

4320 ning kvadrat ildizini chiqarish.

$$x=\frac{-68±12\sqrt{30}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-68±12\sqrt{30}}{-2}$$

x=\frac{-68±12\sqrt{30}}{-2} tenglamasini yeching, bunda ± musbat. -68 ni 12\sqrt{30} ga qo'shish.

$$x=\frac{12\sqrt{30}-68}{-2}$$

-68+12\sqrt{30} ni -2 ga bo'lish.

$$x=34-6\sqrt{30}$$

x=\frac{-68±12\sqrt{30}}{-2} tenglamasini yeching, bunda ± manfiy. -68 dan 12\sqrt{30} ni ayirish.

$$x=\frac{-12\sqrt{30}-68}{-2}$$

-68-12\sqrt{30} ni -2 ga bo'lish.

$$x=6\sqrt{30}+34$$

Tenglama yechildi.

$$x=34-6\sqrt{30} x=6\sqrt{30}+34$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan x^{2} ni ayirish.

$$76x-76-x^{2}=8x$$

Ikkala tarafdan 8x ni ayirish.

$$76x-76-x^{2}-8x=0$$

68x ni olish uchun 76x va -8x ni birlashtirish.

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

76 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

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

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

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

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}+68x}{-1}=\frac{76}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{68}{-1}x=\frac{76}{-1}$$

68 ni -1 ga bo'lish.

$$x^{2}-68x=\frac{76}{-1}$$

76 ni -1 ga bo'lish.

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

-68 ni bo‘lish, x shartining koeffitsienti, 2 ga -34 olish uchun. Keyin, -34 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-68x+\left(-34\right)^{2}=-76+\left(-34\right)^{2}$$

-34 kvadratini chiqarish.

$$x^{2}-68x+1156=-76+1156$$

-76 ni 1156 ga qo'shish.

$$x^{2}-68x+1156=1080$$

x^{2}-68x+1156 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-34\right)^{2}=1080$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-34\right)^{2}}=\sqrt{1080}$$

Qisqartirish.

$$x-34=6\sqrt{30} x-34=-6\sqrt{30}$$

34 ni tenglamaning ikkala tarafiga qo'shish.

$$x=6\sqrt{30}+34 x=34-6\sqrt{30}$$