8x^2+2x-8=52= eching

$$8 { x }^{ 2 } +2x-8=52=$$

x uchun yechish

$$x = \frac{\sqrt{481} - 1}{8} \approx 2,616464025$$

$$x=\frac{-\sqrt{481}-1}{8}\approx -2,866464025$$

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.

$$8x^{2}+2x-8=52$$

Tenglamaning ikkala tarafidan 52 ni ayirish.

$$8x^{2}+2x-8-52=52-52$$

O‘zidan 52 ayirilsa 0 qoladi.

$$8x^{2}+2x-8-52=0$$

-8 dan 52 ni ayirish.

$$8x^{2}+2x-60=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 8 ni a, 2 ni b va -60 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}-4\times 8\left(-60\right)}}{2\times 8}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\times 8\left(-60\right)}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4-32\left(-60\right)}}{2\times 8}$$

-32 ni -60 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+1920}}{2\times 8}$$

4 ni 1920 ga qo'shish.

$$x=\frac{-2±\sqrt{1924}}{2\times 8}$$

1924 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{481}}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{-2±2\sqrt{481}}{16}$$

x=\frac{-2±2\sqrt{481}}{16} tenglamasini yeching, bunda ± musbat. -2 ni 2\sqrt{481} ga qo'shish.

$$x=\frac{2\sqrt{481}-2}{16}$$

-2+2\sqrt{481} ni 16 ga bo'lish.

$$x=\frac{\sqrt{481}-1}{8}$$

x=\frac{-2±2\sqrt{481}}{16} tenglamasini yeching, bunda ± manfiy. -2 dan 2\sqrt{481} ni ayirish.

$$x=\frac{-2\sqrt{481}-2}{16}$$

-2-2\sqrt{481} ni 16 ga bo'lish.

$$x=\frac{-\sqrt{481}-1}{8}$$

Tenglama yechildi.

$$x=\frac{\sqrt{481}-1}{8} x=\frac{-\sqrt{481}-1}{8}$$

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.

$$8x^{2}+2x-8=52$$

8 ni tenglamaning ikkala tarafiga qo'shish.

$$8x^{2}+2x-8-\left(-8\right)=52-\left(-8\right)$$

O‘zidan -8 ayirilsa 0 qoladi.

$$8x^{2}+2x=52-\left(-8\right)$$

52 dan -8 ni ayirish.

$$8x^{2}+2x=60$$

Ikki tarafini 8 ga bo‘ling.

$$\frac{8x^{2}+2x}{8}=\frac{60}{8}$$

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

$$x^{2}+\frac{2}{8}x=\frac{60}{8}$$

\frac{2}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{1}{4}x=\frac{60}{8}$$

\frac{60}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}+\frac{1}{4}x=\frac{15}{2}$$

\frac{1}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{8} olish uchun. Keyin, \frac{1}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{1}{4}x+\left(\frac{1}{8}\right)^{2}=\frac{15}{2}+\left(\frac{1}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{8} kvadratini chiqarish.

$$x^{2}+\frac{1}{4}x+\frac{1}{64}=\frac{15}{2}+\frac{1}{64}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{15}{2} ni \frac{1}{64} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{1}{4}x+\frac{1}{64}=\frac{481}{64}$$

x^{2}+\frac{1}{4}x+\frac{1}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{8}\right)^{2}=\frac{481}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{8}\right)^{2}}=\sqrt{\frac{481}{64}}$$

Qisqartirish.

$$x+\frac{1}{8}=\frac{\sqrt{481}}{8} x+\frac{1}{8}=-\frac{\sqrt{481}}{8}$$

Tenglamaning ikkala tarafidan \frac{1}{8} ni ayirish.

$$x=\frac{\sqrt{481}-1}{8} x=\frac{-\sqrt{481}-1}{8}$$