x^2-2x+28/37=0 eching

$${ x }^{ 2 } -2x+ \frac{ 28 }{ 37 } =0$$

x uchun yechish

$$x=\frac{3\sqrt{37}}{37}+1\approx 1,493196962$$

$$x=-\frac{3\sqrt{37}}{37}+1\approx 0,506803038$$

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.

$$x^{2}-2x+\frac{28}{37}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -2 ni b va \frac{28}{37} ni c bilan almashtiring.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times \frac{28}{37}}}{2}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times \frac{28}{37}}}{2}$$

-4 ni \frac{28}{37} marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4-\frac{112}{37}}}{2}$$

4 ni -\frac{112}{37} ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{\frac{36}{37}}}{2}$$

\frac{36}{37} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±\frac{6\sqrt{37}}{37}}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±\frac{6\sqrt{37}}{37}}{2}$$

x=\frac{2±\frac{6\sqrt{37}}{37}}{2} tenglamasini yeching, bunda ± musbat. 2 ni \frac{6\sqrt{37}}{37} ga qo'shish.

$$x=\frac{\frac{6\sqrt{37}}{37}+2}{2}$$

2+\frac{6\sqrt{37}}{37} ni 2 ga bo'lish.

$$x=\frac{3\sqrt{37}}{37}+1$$

x=\frac{2±\frac{6\sqrt{37}}{37}}{2} tenglamasini yeching, bunda ± manfiy. 2 dan \frac{6\sqrt{37}}{37} ni ayirish.

$$x=\frac{-\frac{6\sqrt{37}}{37}+2}{2}$$

2-\frac{6\sqrt{37}}{37} ni 2 ga bo'lish.

$$x=-\frac{3\sqrt{37}}{37}+1$$

Tenglama yechildi.

$$x=\frac{3\sqrt{37}}{37}+1 x=-\frac{3\sqrt{37}}{37}+1$$

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.

$$x^{2}-2x+\frac{28}{37}=0$$

Tenglamaning ikkala tarafidan \frac{28}{37} ni ayirish.

$$x^{2}-2x+\frac{28}{37}-\frac{28}{37}=-\frac{28}{37}$$

O‘zidan \frac{28}{37} ayirilsa 0 qoladi.

$$x^{2}-2x=-\frac{28}{37}$$

-2 ni bo‘lish, x shartining koeffitsienti, 2 ga -1 olish uchun. Keyin, -1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-2x+1=-\frac{28}{37}+1$$

-\frac{28}{37} ni 1 ga qo'shish.

$$x^{2}-2x+1=\frac{9}{37}$$

x^{2}-2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-1\right)^{2}=\frac{9}{37}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{9}{37}}$$

Qisqartirish.

$$x-1=\frac{3\sqrt{37}}{37} x-1=-\frac{3\sqrt{37}}{37}$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3\sqrt{37}}{37}+1 x=-\frac{3\sqrt{37}}{37}+1$$