x^2+9x-25=0 eching

$$x ^ { 2 } + 9 x - 25 = 0$$

x uchun yechish

$$x = \frac{\sqrt{181} - 9}{2} \approx 2,226812024$$

$$x=\frac{-\sqrt{181}-9}{2}\approx -11,226812024$$

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.

$$x^{2}+9x-25=0$$

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 -25 ni c bilan almashtiring.

$$x=\frac{-9±\sqrt{9^{2}-4\left(-25\right)}}{2}$$

9 kvadratini chiqarish.

$$x=\frac{-9±\sqrt{81-4\left(-25\right)}}{2}$$

-4 ni -25 marotabaga ko'paytirish.

$$x=\frac{-9±\sqrt{81+100}}{2}$$

81 ni 100 ga qo'shish.

$$x=\frac{-9±\sqrt{181}}{2}$$

x=\frac{-9±\sqrt{181}}{2} tenglamasini yeching, bunda ± musbat. -9 ni \sqrt{181} ga qo'shish.

$$x=\frac{\sqrt{181}-9}{2}$$

x=\frac{-9±\sqrt{181}}{2} tenglamasini yeching, bunda ± manfiy. -9 dan \sqrt{181} ni ayirish.

$$x=\frac{-\sqrt{181}-9}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{181}-9}{2} x=\frac{-\sqrt{181}-9}{2}$$

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.

$$x^{2}+9x-25=0$$

25 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}+9x-25-\left(-25\right)=-\left(-25\right)$$

O‘zidan -25 ayirilsa 0 qoladi.

$$x^{2}+9x=-\left(-25\right)$$

0 dan -25 ni ayirish.

$$x^{2}+9x=25$$

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.

$$x^{2}+9x+\left(\frac{9}{2}\right)^{2}=25+\left(\frac{9}{2}\right)^{2}$$

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

$$x^{2}+9x+\frac{81}{4}=25+\frac{81}{4}$$

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

$$x^{2}+9x+\frac{81}{4}=\frac{181}{4}$$

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.

$$\left(x+\frac{9}{2}\right)^{2}=\frac{181}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{9}{2}\right)^{2}}=\sqrt{\frac{181}{4}}$$

Qisqartirish.

$$x+\frac{9}{2}=\frac{\sqrt{181}}{2} x+\frac{9}{2}=-\frac{\sqrt{181}}{2}$$

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

$$x=\frac{\sqrt{181}-9}{2} x=\frac{-\sqrt{181}-9}{2}$$