m^2+26m-15=0 eching

$$m ^ { 2 } + 26 m - 15 = 0$$

m uchun yechish

$$m=2\sqrt{46}-13\approx 0,564659966$$

$$m=-2\sqrt{46}-13\approx -26,564659966$$

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.

$$m^{2}+26m-15=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 26 ni b va -15 ni c bilan almashtiring.

$$m=\frac{-26±\sqrt{26^{2}-4\left(-15\right)}}{2}$$

26 kvadratini chiqarish.

$$m=\frac{-26±\sqrt{676-4\left(-15\right)}}{2}$$

-4 ni -15 marotabaga ko'paytirish.

$$m=\frac{-26±\sqrt{676+60}}{2}$$

676 ni 60 ga qo'shish.

$$m=\frac{-26±\sqrt{736}}{2}$$

736 ning kvadrat ildizini chiqarish.

$$m=\frac{-26±4\sqrt{46}}{2}$$

m=\frac{-26±4\sqrt{46}}{2} tenglamasini yeching, bunda ± musbat. -26 ni 4\sqrt{46} ga qo'shish.

$$m=\frac{4\sqrt{46}-26}{2}$$

-26+4\sqrt{46} ni 2 ga bo'lish.

$$m=2\sqrt{46}-13$$

m=\frac{-26±4\sqrt{46}}{2} tenglamasini yeching, bunda ± manfiy. -26 dan 4\sqrt{46} ni ayirish.

$$m=\frac{-4\sqrt{46}-26}{2}$$

-26-4\sqrt{46} ni 2 ga bo'lish.

$$m=-2\sqrt{46}-13$$

Tenglama yechildi.

$$m=2\sqrt{46}-13 m=-2\sqrt{46}-13$$

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.

$$m^{2}+26m-15=0$$

15 ni tenglamaning ikkala tarafiga qo'shish.

$$m^{2}+26m-15-\left(-15\right)=-\left(-15\right)$$

O‘zidan -15 ayirilsa 0 qoladi.

$$m^{2}+26m=-\left(-15\right)$$

0 dan -15 ni ayirish.

$$m^{2}+26m=15$$

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

$$m^{2}+26m+13^{2}=15+13^{2}$$

13 kvadratini chiqarish.

$$m^{2}+26m+169=15+169$$

15 ni 169 ga qo'shish.

$$m^{2}+26m+169=184$$

m^{2}+26m+169 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(m+13\right)^{2}=184$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m+13\right)^{2}}=\sqrt{184}$$

Qisqartirish.

$$m+13=2\sqrt{46} m+13=-2\sqrt{46}$$

Tenglamaning ikkala tarafidan 13 ni ayirish.

$$m=2\sqrt{46}-13 m=-2\sqrt{46}-13$$