x^2+9x+7=5 eching

$${ x }^{ 2 } +9x+7=5$$

x uchun yechish

$$x=\frac{\sqrt{73}-9}{2}\approx -0,227998127$$

$$x=\frac{-\sqrt{73}-9}{2}\approx -8,772001873$$

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.

$$x^{2}+9x+7=5$$

Tenglamaning ikkala tarafidan 5 ni ayirish.

$$x^{2}+9x+7-5=5-5$$

O‘zidan 5 ayirilsa 0 qoladi.

$$x^{2}+9x+7-5=0$$

7 dan 5 ni ayirish.

$$x^{2}+9x+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 9 ni b va 2 ni c bilan almashtiring.

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

9 kvadratini chiqarish.

$$x=\frac{-9±\sqrt{81-4\times 2}}{2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-9±\sqrt{81-8}}{2}$$

81 ni -8 ga qo'shish.

$$x=\frac{-9±\sqrt{73}}{2}$$

x=\frac{-9±\sqrt{73}}{2} tenglamasini yeching, bunda ± musbat. -9 ni \sqrt{73} ga qo'shish.

$$x=\frac{\sqrt{73}-9}{2}$$

x=\frac{-9±\sqrt{73}}{2} tenglamasini yeching, bunda ± manfiy. -9 dan \sqrt{73} ni ayirish.

$$x=\frac{-\sqrt{73}-9}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{73}-9}{2} x=\frac{-\sqrt{73}-9}{2}$$

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.

$$x^{2}+9x+7=5$$

Tenglamaning ikkala tarafidan 7 ni ayirish.

$$x^{2}+9x+7-7=5-7$$

O‘zidan 7 ayirilsa 0 qoladi.

$$x^{2}+9x=5-7$$

5 dan 7 ni ayirish.

$$x^{2}+9x=-2$$

9 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{9}{2} olish uchun. Keyin, \frac{9}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+9x+\left(\frac{9}{2}\right)^{2}=-2+\left(\frac{9}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{9}{2} kvadratini chiqarish.

$$x^{2}+9x+\frac{81}{4}=-2+\frac{81}{4}$$

-2 ni \frac{81}{4} ga qo'shish.

$$x^{2}+9x+\frac{81}{4}=\frac{73}{4}$$

x^{2}+9x+\frac{81}{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.

$$\left(x+\frac{9}{2}\right)^{2}=\frac{73}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{9}{2}\right)^{2}}=\sqrt{\frac{73}{4}}$$

Qisqartirish.

$$x+\frac{9}{2}=\frac{\sqrt{73}}{2} x+\frac{9}{2}=-\frac{\sqrt{73}}{2}$$

Tenglamaning ikkala tarafidan \frac{9}{2} ni ayirish.

$$x=\frac{\sqrt{73}-9}{2} x=\frac{-\sqrt{73}-9}{2}$$