72x=8x^2-1552 eching

$$72 x = 8 x ^ { 2 } - 1552$$

x uchun yechish

$$x = \frac{\sqrt{857} + 9}{2} \approx 19,137281168$$

$$x=\frac{9-\sqrt{857}}{2}\approx -10,137281168$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 8x^{2} ni ayirish.

$$72x-8x^{2}=-1552$$

1552 ni ikki tarafga qo’shing.

$$72x-8x^{2}+1552=0$$

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.

$$-8x^{2}+72x+1552=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -8 ni a, 72 ni b va 1552 ni c bilan almashtiring.

$$x=\frac{-72±\sqrt{72^{2}-4\left(-8\right)\times 1552}}{2\left(-8\right)}$$

72 kvadratini chiqarish.

$$x=\frac{-72±\sqrt{5184-4\left(-8\right)\times 1552}}{2\left(-8\right)}$$

-4 ni -8 marotabaga ko'paytirish.

$$x=\frac{-72±\sqrt{5184+32\times 1552}}{2\left(-8\right)}$$

32 ni 1552 marotabaga ko'paytirish.

$$x=\frac{-72±\sqrt{5184+49664}}{2\left(-8\right)}$$

5184 ni 49664 ga qo'shish.

$$x=\frac{-72±\sqrt{54848}}{2\left(-8\right)}$$

54848 ning kvadrat ildizini chiqarish.

$$x=\frac{-72±8\sqrt{857}}{2\left(-8\right)}$$

2 ni -8 marotabaga ko'paytirish.

$$x=\frac{-72±8\sqrt{857}}{-16}$$

x=\frac{-72±8\sqrt{857}}{-16} tenglamasini yeching, bunda ± musbat. -72 ni 8\sqrt{857} ga qo'shish.

$$x=\frac{8\sqrt{857}-72}{-16}$$

-72+8\sqrt{857} ni -16 ga bo'lish.

$$x=\frac{9-\sqrt{857}}{2}$$

x=\frac{-72±8\sqrt{857}}{-16} tenglamasini yeching, bunda ± manfiy. -72 dan 8\sqrt{857} ni ayirish.

$$x=\frac{-8\sqrt{857}-72}{-16}$$

-72-8\sqrt{857} ni -16 ga bo'lish.

$$x=\frac{\sqrt{857}+9}{2}$$

Tenglama yechildi.

$$x=\frac{9-\sqrt{857}}{2} x=\frac{\sqrt{857}+9}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 8x^{2} ni ayirish.

$$72x-8x^{2}=-1552$$

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

$$-8x^{2}+72x=-1552$$

Ikki tarafini -8 ga bo‘ling.

$$\frac{-8x^{2}+72x}{-8}=-\frac{1552}{-8}$$

-8 ga bo'lish -8 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{72}{-8}x=-\frac{1552}{-8}$$

72 ni -8 ga bo'lish.

$$x^{2}-9x=-\frac{1552}{-8}$$

-1552 ni -8 ga bo'lish.

$$x^{2}-9x=194$$

-9 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{2} olish uchun. Keyin, -\frac{9}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-9x+\left(-\frac{9}{2}\right)^{2}=194+\left(-\frac{9}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{2} kvadratini chiqarish.

$$x^{2}-9x+\frac{81}{4}=194+\frac{81}{4}$$

194 ni \frac{81}{4} ga qo'shish.

$$x^{2}-9x+\frac{81}{4}=\frac{857}{4}$$

x^{2}-9x+\frac{81}{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.

$$\left(x-\frac{9}{2}\right)^{2}=\frac{857}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{9}{2}\right)^{2}}=\sqrt{\frac{857}{4}}$$

Qisqartirish.

$$x-\frac{9}{2}=\frac{\sqrt{857}}{2} x-\frac{9}{2}=-\frac{\sqrt{857}}{2}$$

\frac{9}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{857}+9}{2} x=\frac{9-\sqrt{857}}{2}$$