x^2-11x+56=5x+13 eching

$${ x }^{ 2 } -11x+56=5x+13$$

x uchun yechish

$$x=\sqrt{21}+8\approx 12,582575695$$

$$x=8-\sqrt{21}\approx 3,417424305$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 5x ni ayirish.

$$x^{2}-11x+56-5x=13$$

-16x ni olish uchun -11x va -5x ni birlashtirish.

$$x^{2}-16x+56=13$$

Ikkala tarafdan 13 ni ayirish.

$$x^{2}-16x+56-13=0$$

43 olish uchun 56 dan 13 ni ayirish.

$$x^{2}-16x+43=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -16 ni b va 43 ni c bilan almashtiring.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 43}}{2}$$

-16 kvadratini chiqarish.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\times 43}}{2}$$

-4 ni 43 marotabaga ko'paytirish.

$$x=\frac{-\left(-16\right)±\sqrt{256-172}}{2}$$

256 ni -172 ga qo'shish.

$$x=\frac{-\left(-16\right)±\sqrt{84}}{2}$$

84 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-16\right)±2\sqrt{21}}{2}$$

-16 ning teskarisi 16 ga teng.

$$x=\frac{16±2\sqrt{21}}{2}$$

x=\frac{16±2\sqrt{21}}{2} tenglamasini yeching, bunda ± musbat. 16 ni 2\sqrt{21} ga qo'shish.

$$x=\frac{2\sqrt{21}+16}{2}$$

16+2\sqrt{21} ni 2 ga bo'lish.

$$x=\sqrt{21}+8$$

x=\frac{16±2\sqrt{21}}{2} tenglamasini yeching, bunda ± manfiy. 16 dan 2\sqrt{21} ni ayirish.

$$x=\frac{16-2\sqrt{21}}{2}$$

16-2\sqrt{21} ni 2 ga bo'lish.

$$x=8-\sqrt{21}$$

Tenglama yechildi.

$$x=\sqrt{21}+8 x=8-\sqrt{21}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 5x ni ayirish.

$$x^{2}-11x+56-5x=13$$

-16x ni olish uchun -11x va -5x ni birlashtirish.

$$x^{2}-16x+56=13$$

Ikkala tarafdan 56 ni ayirish.

$$x^{2}-16x=13-56$$

-43 olish uchun 13 dan 56 ni ayirish.

$$x^{2}-16x=-43$$

-16 ni bo‘lish, x shartining koeffitsienti, 2 ga -8 olish uchun. Keyin, -8 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-16x+\left(-8\right)^{2}=-43+\left(-8\right)^{2}$$

-8 kvadratini chiqarish.

$$x^{2}-16x+64=-43+64$$

-43 ni 64 ga qo'shish.

$$x^{2}-16x+64=21$$

x^{2}-16x+64 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-8\right)^{2}=21$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{21}$$

Qisqartirish.

$$x-8=\sqrt{21} x-8=-\sqrt{21}$$

8 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{21}+8 x=8-\sqrt{21}$$