x^2+7x-12=0 eching

$$x ^ { 2 } + 7 x - 12 = 0$$

x uchun yechish

$$x = \frac{\sqrt{97} - 7}{2} \approx 1,424428901$$

$$x=\frac{-\sqrt{97}-7}{2}\approx -8,424428901$$

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.

$$x^{2}+7x-12=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 7 ni b va -12 ni c bilan almashtiring.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-12\right)}}{2}$$

7 kvadratini chiqarish.

$$x=\frac{-7±\sqrt{49-4\left(-12\right)}}{2}$$

-4 ni -12 marotabaga ko'paytirish.

$$x=\frac{-7±\sqrt{49+48}}{2}$$

49 ni 48 ga qo'shish.

$$x=\frac{-7±\sqrt{97}}{2}$$

x=\frac{-7±\sqrt{97}}{2} tenglamasini yeching, bunda ± musbat. -7 ni \sqrt{97} ga qo'shish.

$$x=\frac{\sqrt{97}-7}{2}$$

x=\frac{-7±\sqrt{97}}{2} tenglamasini yeching, bunda ± manfiy. -7 dan \sqrt{97} ni ayirish.

$$x=\frac{-\sqrt{97}-7}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{97}-7}{2} x=\frac{-\sqrt{97}-7}{2}$$

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.

$$x^{2}+7x-12=0$$

12 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+7x-12-\left(-12\right)=-\left(-12\right)$$

O‘zidan -12 ayirilsa 0 qoladi.

$$x^{2}+7x=-\left(-12\right)$$

0 dan -12 ni ayirish.

$$x^{2}+7x=12$$

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

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=12+\left(\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{2} kvadratini chiqarish.

$$x^{2}+7x+\frac{49}{4}=12+\frac{49}{4}$$

12 ni \frac{49}{4} ga qo'shish.

$$x^{2}+7x+\frac{49}{4}=\frac{97}{4}$$

x^{2}+7x+\frac{49}{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.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{97}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{97}{4}}$$

Qisqartirish.

$$x+\frac{7}{2}=\frac{\sqrt{97}}{2} x+\frac{7}{2}=-\frac{\sqrt{97}}{2}$$

Tenglamaning ikkala tarafidan \frac{7}{2} ni ayirish.

$$x=\frac{\sqrt{97}-7}{2} x=\frac{-\sqrt{97}-7}{2}$$