10x^2-65x+075=0 eching

$$10 x ^ { 2 } - 65 x + 075 = 0$$

x uchun yechish

$$x = \frac{13}{2} = 6\frac{1}{2} = 6,5$$

$$x=0$$

Faktorlash qadamlari

0 hosil qilish uchun 0 va 75 ni ko'paytirish.

$$10x^{2}-65x+0=0$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$10x^{2}-65x=0$$

x omili.

$$x\left(10x-65\right)=0$$

Tenglamani yechish uchun x=0 va 10x-65=0 ni yeching.

$$x=0 x=\frac{13}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 75 ni ko'paytirish.

$$10x^{2}-65x+0=0$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$10x^{2}-65x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 10 ni a, -65 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-65\right)±\sqrt{\left(-65\right)^{2}}}{2\times 10}$$

\left(-65\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-65\right)±65}{2\times 10}$$

-65 ning teskarisi 65 ga teng.

$$x=\frac{65±65}{2\times 10}$$

2 ni 10 marotabaga ko'paytirish.

$$x=\frac{65±65}{20}$$

x=\frac{65±65}{20} tenglamasini yeching, bunda ± musbat. 65 ni 65 ga qo'shish.

$$x=\frac{130}{20}$$

\frac{130}{20} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{13}{2}$$

x=\frac{65±65}{20} tenglamasini yeching, bunda ± manfiy. 65 dan 65 ni ayirish.

$$x=\frac{0}{20}$$

0 ni 20 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{13}{2} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 75 ni ko'paytirish.

$$10x^{2}-65x+0=0$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$10x^{2}-65x=0$$

Ikki tarafini 10 ga bo‘ling.

$$\frac{10x^{2}-65x}{10}=\frac{0}{10}$$

10 ga bo'lish 10 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{65}{10}\right)x=\frac{0}{10}$$

\frac{-65}{10} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{13}{2}x=\frac{0}{10}$$

0 ni 10 ga bo'lish.

$$x^{2}-\frac{13}{2}x=0$$

-\frac{13}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{13}{4} olish uchun. Keyin, -\frac{13}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{13}{4} kvadratini chiqarish.

$$x^{2}-\frac{13}{2}x+\frac{169}{16}=\frac{169}{16}$$

x^{2}-\frac{13}{2}x+\frac{169}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{13}{4}\right)^{2}=\frac{169}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{13}{4}\right)^{2}}=\sqrt{\frac{169}{16}}$$

Qisqartirish.

$$x-\frac{13}{4}=\frac{13}{4} x-\frac{13}{4}=-\frac{13}{4}$$

\frac{13}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{13}{2} x=0$$