x^2+3x-7/4=0 eching

$$x ^ { 2 } + 3 x - \frac { 7 } { 4 } = 0$$

x uchun yechish

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3,5$$

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

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.

$$x^{2}+3x-\frac{7}{4}=0$$

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{7}{4} ni c bilan almashtiring.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-\frac{7}{4}\right)}}{2}$$

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\left(-\frac{7}{4}\right)}}{2}$$

-4 ni -\frac{7}{4} marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+7}}{2}$$

9 ni 7 ga qo'shish.

$$x=\frac{-3±\sqrt{16}}{2}$$

16 ning kvadrat ildizini chiqarish.

$$x=\frac{-3±4}{2}$$

x=\frac{-3±4}{2} tenglamasini yeching, bunda ± musbat. -3 ni 4 ga qo'shish.

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

x=\frac{-3±4}{2} tenglamasini yeching, bunda ± manfiy. -3 dan 4 ni ayirish.

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

Tenglama yechildi.

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

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.

$$x^{2}+3x-\frac{7}{4}=0$$

\frac{7}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+3x-\frac{7}{4}-\left(-\frac{7}{4}\right)=-\left(-\frac{7}{4}\right)$$

O‘zidan -\frac{7}{4} ayirilsa 0 qoladi.

$$x^{2}+3x=-\left(-\frac{7}{4}\right)$$

0 dan -\frac{7}{4} ni ayirish.

$$x^{2}+3x=\frac{7}{4}$$

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.

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=\frac{7}{4}+\left(\frac{3}{2}\right)^{2}$$

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

$$x^{2}+3x+\frac{9}{4}=\frac{7+9}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{7}{4} ni \frac{9}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

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

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