4x^2+4x-7=930 eching

$$4 { x }^{ 2 } +4x-7=930$$

x uchun yechish

$$x = \frac{\sqrt{938} - 1}{2} \approx 14,813392831$$

$$x=\frac{-\sqrt{938}-1}{2}\approx -15,813392831$$

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.

$$4x^{2}+4x-7=930$$

Tenglamaning ikkala tarafidan 930 ni ayirish.

$$4x^{2}+4x-7-930=930-930$$

O‘zidan 930 ayirilsa 0 qoladi.

$$4x^{2}+4x-7-930=0$$

-7 dan 930 ni ayirish.

$$4x^{2}+4x-937=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, 4 ni b va -937 ni c bilan almashtiring.

$$x=\frac{-4±\sqrt{4^{2}-4\times 4\left(-937\right)}}{2\times 4}$$

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\times 4\left(-937\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16-16\left(-937\right)}}{2\times 4}$$

-16 ni -937 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+14992}}{2\times 4}$$

16 ni 14992 ga qo'shish.

$$x=\frac{-4±\sqrt{15008}}{2\times 4}$$

15008 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±4\sqrt{938}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{-4±4\sqrt{938}}{8}$$

x=\frac{-4±4\sqrt{938}}{8} tenglamasini yeching, bunda ± musbat. -4 ni 4\sqrt{938} ga qo'shish.

$$x=\frac{4\sqrt{938}-4}{8}$$

-4+4\sqrt{938} ni 8 ga bo'lish.

$$x=\frac{\sqrt{938}-1}{2}$$

x=\frac{-4±4\sqrt{938}}{8} tenglamasini yeching, bunda ± manfiy. -4 dan 4\sqrt{938} ni ayirish.

$$x=\frac{-4\sqrt{938}-4}{8}$$

-4-4\sqrt{938} ni 8 ga bo'lish.

$$x=\frac{-\sqrt{938}-1}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{938}-1}{2} x=\frac{-\sqrt{938}-1}{2}$$

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.

$$4x^{2}+4x-7=930$$

7 ni tenglamaning ikkala tarafiga qo'shish.

$$4x^{2}+4x-7-\left(-7\right)=930-\left(-7\right)$$

O‘zidan -7 ayirilsa 0 qoladi.

$$4x^{2}+4x=930-\left(-7\right)$$

930 dan -7 ni ayirish.

$$4x^{2}+4x=937$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}+4x}{4}=\frac{937}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{4}{4}x=\frac{937}{4}$$

4 ni 4 ga bo'lish.

$$x^{2}+x=\frac{937}{4}$$

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

$$x^{2}+x+\left(\frac{1}{2}\right)^{2}=\frac{937}{4}+\left(\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{2} kvadratini chiqarish.

$$x^{2}+x+\frac{1}{4}=\frac{937+1}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{937}{4} ni \frac{1}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+x+\frac{1}{4}=\frac{469}{2}$$

x^{2}+x+\frac{1}{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.

$$\left(x+\frac{1}{2}\right)^{2}=\frac{469}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{469}{2}}$$

Qisqartirish.

$$x+\frac{1}{2}=\frac{\sqrt{938}}{2} x+\frac{1}{2}=-\frac{\sqrt{938}}{2}$$

Tenglamaning ikkala tarafidan \frac{1}{2} ni ayirish.

$$x=\frac{\sqrt{938}-1}{2} x=\frac{-\sqrt{938}-1}{2}$$