x^2+13x=2 eching

$$x ^ { 2 } + 13 x = 2$$

x uchun yechish

$$x=\frac{\sqrt{177}-13}{2}\approx 0,152067348$$

$$x=\frac{-\sqrt{177}-13}{2}\approx -13,152067348$$

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.

$$x^{2}+13x=2$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x^{2}+13x-2=2-2$$

O‘zidan 2 ayirilsa 0 qoladi.

$$x^{2}+13x-2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 13 ni b va -2 ni c bilan almashtiring.

$$x=\frac{-13±\sqrt{13^{2}-4\left(-2\right)}}{2}$$

13 kvadratini chiqarish.

$$x=\frac{-13±\sqrt{169-4\left(-2\right)}}{2}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-13±\sqrt{169+8}}{2}$$

169 ni 8 ga qo'shish.

$$x=\frac{-13±\sqrt{177}}{2}$$

x=\frac{-13±\sqrt{177}}{2} tenglamasini yeching, bunda ± musbat. -13 ni \sqrt{177} ga qo'shish.

$$x=\frac{\sqrt{177}-13}{2}$$

x=\frac{-13±\sqrt{177}}{2} tenglamasini yeching, bunda ± manfiy. -13 dan \sqrt{177} ni ayirish.

$$x=\frac{-\sqrt{177}-13}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{177}-13}{2} x=\frac{-\sqrt{177}-13}{2}$$

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.

$$x^{2}+13x=2$$

13 ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{13}{2} olish uchun. Keyin, \frac{13}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+13x+\left(\frac{13}{2}\right)^{2}=2+\left(\frac{13}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{13}{2} kvadratini chiqarish.

$$x^{2}+13x+\frac{169}{4}=2+\frac{169}{4}$$

2 ni \frac{169}{4} ga qo'shish.

$$x^{2}+13x+\frac{169}{4}=\frac{177}{4}$$

x^{2}+13x+\frac{169}{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.

$$\left(x+\frac{13}{2}\right)^{2}=\frac{177}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{13}{2}\right)^{2}}=\sqrt{\frac{177}{4}}$$

Qisqartirish.

$$x+\frac{13}{2}=\frac{\sqrt{177}}{2} x+\frac{13}{2}=-\frac{\sqrt{177}}{2}$$

Tenglamaning ikkala tarafidan \frac{13}{2} ni ayirish.

$$x=\frac{\sqrt{177}-13}{2} x=\frac{-\sqrt{177}-13}{2}$$