x^2+2x+4=22x+9 eching

$${ x }^{ 2 } +2x+4=22x+9$$

x uchun yechish

$$x=\sqrt{105}+10\approx 20,246950766$$

$$x=10-\sqrt{105}\approx -0,246950766$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 22x ni ayirish.

$$x^{2}+2x+4-22x=9$$

-20x ni olish uchun 2x va -22x ni birlashtirish.

$$x^{2}-20x+4=9$$

Ikkala tarafdan 9 ni ayirish.

$$x^{2}-20x+4-9=0$$

-5 olish uchun 4 dan 9 ni ayirish.

$$x^{2}-20x-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -20 ni b va -5 ni c bilan almashtiring.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\left(-5\right)}}{2}$$

-20 kvadratini chiqarish.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\left(-5\right)}}{2}$$

-4 ni -5 marotabaga ko'paytirish.

$$x=\frac{-\left(-20\right)±\sqrt{400+20}}{2}$$

400 ni 20 ga qo'shish.

$$x=\frac{-\left(-20\right)±\sqrt{420}}{2}$$

420 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-20\right)±2\sqrt{105}}{2}$$

-20 ning teskarisi 20 ga teng.

$$x=\frac{20±2\sqrt{105}}{2}$$

x=\frac{20±2\sqrt{105}}{2} tenglamasini yeching, bunda ± musbat. 20 ni 2\sqrt{105} ga qo'shish.

$$x=\frac{2\sqrt{105}+20}{2}$$

20+2\sqrt{105} ni 2 ga bo'lish.

$$x=\sqrt{105}+10$$

x=\frac{20±2\sqrt{105}}{2} tenglamasini yeching, bunda ± manfiy. 20 dan 2\sqrt{105} ni ayirish.

$$x=\frac{20-2\sqrt{105}}{2}$$

20-2\sqrt{105} ni 2 ga bo'lish.

$$x=10-\sqrt{105}$$

Tenglama yechildi.

$$x=\sqrt{105}+10 x=10-\sqrt{105}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 22x ni ayirish.

$$x^{2}+2x+4-22x=9$$

-20x ni olish uchun 2x va -22x ni birlashtirish.

$$x^{2}-20x+4=9$$

Ikkala tarafdan 4 ni ayirish.

$$x^{2}-20x=9-4$$

5 olish uchun 9 dan 4 ni ayirish.

$$x^{2}-20x=5$$

-20 ni bo‘lish, x shartining koeffitsienti, 2 ga -10 olish uchun. Keyin, -10 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-20x+\left(-10\right)^{2}=5+\left(-10\right)^{2}$$

-10 kvadratini chiqarish.

$$x^{2}-20x+100=5+100$$

5 ni 100 ga qo'shish.

$$x^{2}-20x+100=105$$

x^{2}-20x+100 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-10\right)^{2}=105$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-10\right)^{2}}=\sqrt{105}$$

Qisqartirish.

$$x-10=\sqrt{105} x-10=-\sqrt{105}$$

10 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{105}+10 x=10-\sqrt{105}$$