x^2-7x-9=0 eching

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

x uchun yechish

$$x = \frac{\sqrt{85} + 7}{2} \approx 8,109772229$$

$$x=\frac{7-\sqrt{85}}{2}\approx -1,109772229$$

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.

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

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 -9 ni c bilan almashtiring.

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

-7 kvadratini chiqarish.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\left(-9\right)}}{2}$$

-4 ni -9 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49+36}}{2}$$

49 ni 36 ga qo'shish.

$$x=\frac{-\left(-7\right)±\sqrt{85}}{2}$$

-7 ning teskarisi 7 ga teng.

$$x=\frac{7±\sqrt{85}}{2}$$

x=\frac{7±\sqrt{85}}{2} tenglamasini yeching, bunda ± musbat. 7 ni \sqrt{85} ga qo'shish.

$$x=\frac{\sqrt{85}+7}{2}$$

x=\frac{7±\sqrt{85}}{2} tenglamasini yeching, bunda ± manfiy. 7 dan \sqrt{85} ni ayirish.

$$x=\frac{7-\sqrt{85}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{85}+7}{2} x=\frac{7-\sqrt{85}}{2}$$

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.

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

9 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-7x-9-\left(-9\right)=-\left(-9\right)$$

O‘zidan -9 ayirilsa 0 qoladi.

$$x^{2}-7x=-\left(-9\right)$$

0 dan -9 ni ayirish.

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

-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.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=9+\left(-\frac{7}{2}\right)^{2}$$

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

$$x^{2}-7x+\frac{49}{4}=9+\frac{49}{4}$$

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

$$x^{2}-7x+\frac{49}{4}=\frac{85}{4}$$

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.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{85}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{85}{4}}$$

Qisqartirish.

$$x-\frac{7}{2}=\frac{\sqrt{85}}{2} x-\frac{7}{2}=-\frac{\sqrt{85}}{2}$$

\frac{7}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{85}+7}{2} x=\frac{7-\sqrt{85}}{2}$$