7x^2=52+x) eching

$$7 { x }^{ 2 } =52+x)$$

x uchun yechish

$$x = \frac{\sqrt{1457} + 1}{14} \approx 2,797904955$$

$$x=\frac{1-\sqrt{1457}}{14}\approx -2,655047812$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 52 ni ayirish.

$$7x^{2}-52=x$$

Ikkala tarafdan x ni ayirish.

$$7x^{2}-52-x=0$$

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.

$$7x^{2}-x-52=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 7 ni a, -1 ni b va -52 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 7\left(-52\right)}}{2\times 7}$$

-4 ni 7 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1-28\left(-52\right)}}{2\times 7}$$

-28 ni -52 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+1456}}{2\times 7}$$

1 ni 1456 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{1457}}{2\times 7}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±\sqrt{1457}}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{1±\sqrt{1457}}{14}$$

x=\frac{1±\sqrt{1457}}{14} tenglamasini yeching, bunda ± musbat. 1 ni \sqrt{1457} ga qo'shish.

$$x=\frac{\sqrt{1457}+1}{14}$$

x=\frac{1±\sqrt{1457}}{14} tenglamasini yeching, bunda ± manfiy. 1 dan \sqrt{1457} ni ayirish.

$$x=\frac{1-\sqrt{1457}}{14}$$

Tenglama yechildi.

$$x=\frac{\sqrt{1457}+1}{14} x=\frac{1-\sqrt{1457}}{14}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan x ni ayirish.

$$7x^{2}-x=52$$

Ikki tarafini 7 ga bo‘ling.

$$\frac{7x^{2}-x}{7}=\frac{52}{7}$$

7 ga bo'lish 7 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{1}{7}x=\frac{52}{7}$$

-\frac{1}{7} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{14} olish uchun. Keyin, -\frac{1}{14} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{7}x+\left(-\frac{1}{14}\right)^{2}=\frac{52}{7}+\left(-\frac{1}{14}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{14} kvadratini chiqarish.

$$x^{2}-\frac{1}{7}x+\frac{1}{196}=\frac{52}{7}+\frac{1}{196}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{52}{7} ni \frac{1}{196} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{1}{7}x+\frac{1}{196}=\frac{1457}{196}$$

x^{2}-\frac{1}{7}x+\frac{1}{196} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{14}\right)^{2}=\frac{1457}{196}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{14}\right)^{2}}=\sqrt{\frac{1457}{196}}$$

Qisqartirish.

$$x-\frac{1}{14}=\frac{\sqrt{1457}}{14} x-\frac{1}{14}=-\frac{\sqrt{1457}}{14}$$

\frac{1}{14} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{1457}+1}{14} x=\frac{1-\sqrt{1457}}{14}$$