x^2+x+1=25x+2 eching

$$x ^ { 2 } + x + 1 = 25 x + 2$$

x uchun yechish

$$x=\sqrt{145}+12\approx 24,041594579$$

$$x=12-\sqrt{145}\approx -0,041594579$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 25x ni ayirish.

$$x^{2}+x+1-25x=2$$

-24x ni olish uchun x va -25x ni birlashtirish.

$$x^{2}-24x+1=2$$

Ikkala tarafdan 2 ni ayirish.

$$x^{2}-24x+1-2=0$$

-1 olish uchun 1 dan 2 ni ayirish.

$$x^{2}-24x-1=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -24 ni b va -1 ni c bilan almashtiring.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\left(-1\right)}}{2}$$

-24 kvadratini chiqarish.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\left(-1\right)}}{2}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-24\right)±\sqrt{576+4}}{2}$$

576 ni 4 ga qo'shish.

$$x=\frac{-\left(-24\right)±\sqrt{580}}{2}$$

580 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-24\right)±2\sqrt{145}}{2}$$

-24 ning teskarisi 24 ga teng.

$$x=\frac{24±2\sqrt{145}}{2}$$

x=\frac{24±2\sqrt{145}}{2} tenglamasini yeching, bunda ± musbat. 24 ni 2\sqrt{145} ga qo'shish.

$$x=\frac{2\sqrt{145}+24}{2}$$

24+2\sqrt{145} ni 2 ga bo'lish.

$$x=\sqrt{145}+12$$

x=\frac{24±2\sqrt{145}}{2} tenglamasini yeching, bunda ± manfiy. 24 dan 2\sqrt{145} ni ayirish.

$$x=\frac{24-2\sqrt{145}}{2}$$

24-2\sqrt{145} ni 2 ga bo'lish.

$$x=12-\sqrt{145}$$

Tenglama yechildi.

$$x=\sqrt{145}+12 x=12-\sqrt{145}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 25x ni ayirish.

$$x^{2}+x+1-25x=2$$

-24x ni olish uchun x va -25x ni birlashtirish.

$$x^{2}-24x+1=2$$

Ikkala tarafdan 1 ni ayirish.

$$x^{2}-24x=2-1$$

1 olish uchun 2 dan 1 ni ayirish.

$$x^{2}-24x=1$$

-24 ni bo‘lish, x shartining koeffitsienti, 2 ga -12 olish uchun. Keyin, -12 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-24x+\left(-12\right)^{2}=1+\left(-12\right)^{2}$$

-12 kvadratini chiqarish.

$$x^{2}-24x+144=1+144$$

1 ni 144 ga qo'shish.

$$x^{2}-24x+144=145$$

x^{2}-24x+144 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-12\right)^{2}=145$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-12\right)^{2}}=\sqrt{145}$$

Qisqartirish.

$$x-12=\sqrt{145} x-12=-\sqrt{145}$$

12 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{145}+12 x=12-\sqrt{145}$$