x^2+3x+5/4=0 eching

$$x ^ { 2 } + 3 x + \frac { 5 } { 4 } = 0$$

x uchun yechish

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2,5$$

$$x=-\frac{1}{2}=-0,5$$

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.

$$x^{2}+3x+\frac{5}{4}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 3 ni b va \frac{5}{4} ni c bilan almashtiring.

$$x=\frac{-3±\sqrt{3^{2}-4\times \frac{5}{4}}}{2}$$

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\times \frac{5}{4}}}{2}$$

-4 ni \frac{5}{4} marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9-5}}{2}$$

9 ni -5 ga qo'shish.

$$x=\frac{-3±\sqrt{4}}{2}$$

4 ning kvadrat ildizini chiqarish.

$$x=\frac{-3±2}{2}$$

x=\frac{-3±2}{2} tenglamasini yeching, bunda ± musbat. -3 ni 2 ga qo'shish.

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

x=\frac{-3±2}{2} tenglamasini yeching, bunda ± manfiy. -3 dan 2 ni ayirish.

$$x=-\frac{5}{2}$$

Tenglama yechildi.

$$x=-\frac{1}{2} x=-\frac{5}{2}$$

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.

$$x^{2}+3x+\frac{5}{4}=0$$

Tenglamaning ikkala tarafidan \frac{5}{4} ni ayirish.

$$x^{2}+3x+\frac{5}{4}-\frac{5}{4}=-\frac{5}{4}$$

O‘zidan \frac{5}{4} ayirilsa 0 qoladi.

$$x^{2}+3x=-\frac{5}{4}$$

3 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{2} olish uchun. Keyin, \frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=-\frac{5}{4}+\left(\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{2} kvadratini chiqarish.

$$x^{2}+3x+\frac{9}{4}=\frac{-5+9}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{5}{4} ni \frac{9}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+3x+\frac{9}{4}=1$$

x^{2}+3x+\frac{9}{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.

$$\left(x+\frac{3}{2}\right)^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{1}$$

Qisqartirish.

$$x+\frac{3}{2}=1 x+\frac{3}{2}=-1$$

Tenglamaning ikkala tarafidan \frac{3}{2} ni ayirish.

$$x=-\frac{1}{2} x=-\frac{5}{2}$$