26x^2+25x*59=0 eching

$$26 { x }^{ 2 } +25x \times 59=0$$

x uchun yechish

$$x = -\frac{1475}{26} = -56\frac{19}{26} \approx -56,730769231$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(26x+25\times 59\right)=0$$

Tenglamani yechish uchun x=0 va 26x+1475=0 ni yeching.

$$x=0 x=-\frac{1475}{26}$$

Kvadrat tenglamalaridan foydalanish qoidalari

1475 hosil qilish uchun 25 va 59 ni ko'paytirish.

$$26x^{2}+1475x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 26 ni a, 1475 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-1475±\sqrt{1475^{2}}}{2\times 26}$$

1475^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-1475±1475}{2\times 26}$$

2 ni 26 marotabaga ko'paytirish.

$$x=\frac{-1475±1475}{52}$$

x=\frac{-1475±1475}{52} tenglamasini yeching, bunda ± musbat. -1475 ni 1475 ga qo'shish.

$$x=\frac{0}{52}$$

0 ni 52 ga bo'lish.

$$x=0$$

x=\frac{-1475±1475}{52} tenglamasini yeching, bunda ± manfiy. -1475 dan 1475 ni ayirish.

$$x=-\frac{2950}{52}$$

\frac{-2950}{52} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1475}{26}$$

Tenglama yechildi.

$$x=0 x=-\frac{1475}{26}$$

Kvadratni yakunlash bo'yicha qadamlar

1475 hosil qilish uchun 25 va 59 ni ko'paytirish.

$$26x^{2}+1475x=0$$

Ikki tarafini 26 ga bo‘ling.

$$\frac{26x^{2}+1475x}{26}=\frac{0}{26}$$

26 ga bo'lish 26 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{1475}{26}x=\frac{0}{26}$$

0 ni 26 ga bo'lish.

$$x^{2}+\frac{1475}{26}x=0$$

\frac{1475}{26} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1475}{52} olish uchun. Keyin, \frac{1475}{52} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{1475}{26}x+\left(\frac{1475}{52}\right)^{2}=\left(\frac{1475}{52}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1475}{52} kvadratini chiqarish.

$$x^{2}+\frac{1475}{26}x+\frac{2175625}{2704}=\frac{2175625}{2704}$$

x^{2}+\frac{1475}{26}x+\frac{2175625}{2704} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1475}{52}\right)^{2}=\frac{2175625}{2704}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1475}{52}\right)^{2}}=\sqrt{\frac{2175625}{2704}}$$

Qisqartirish.

$$x+\frac{1475}{52}=\frac{1475}{52} x+\frac{1475}{52}=-\frac{1475}{52}$$

Tenglamaning ikkala tarafidan \frac{1475}{52} ni ayirish.

$$x=0 x=-\frac{1475}{26}$$