x^2-18x=-2x+64 eching

$$x ^ { 2 } - 18 x = - 2 x + 64$$

x uchun yechish

$$x=8\sqrt{2}+8\approx 19,313708499$$

$$x=8-8\sqrt{2}\approx -3,313708499$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x ni ikki tarafga qo’shing.

$$x^{2}-18x+2x=64$$

-16x ni olish uchun -18x va 2x ni birlashtirish.

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

Ikkala tarafdan 64 ni ayirish.

$$x^{2}-16x-64=0$$

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 -64 ni c bilan almashtiring.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-64\right)}}{2}$$

-16 kvadratini chiqarish.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\left(-64\right)}}{2}$$

-4 ni -64 marotabaga ko'paytirish.

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

256 ni 256 ga qo'shish.

$$x=\frac{-\left(-16\right)±\sqrt{512}}{2}$$

512 ning kvadrat ildizini chiqarish.

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

-16 ning teskarisi 16 ga teng.

$$x=\frac{16±16\sqrt{2}}{2}$$

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

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

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

$$x=8\sqrt{2}+8$$

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

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

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

$$x=8-8\sqrt{2}$$

Tenglama yechildi.

$$x=8\sqrt{2}+8 x=8-8\sqrt{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2x ni ikki tarafga qo’shing.

$$x^{2}-18x+2x=64$$

-16x ni olish uchun -18x va 2x ni birlashtirish.

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

-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.

$$x^{2}-16x+\left(-8\right)^{2}=64+\left(-8\right)^{2}$$

-8 kvadratini chiqarish.

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

64 ni 64 ga qo'shish.

$$x^{2}-16x+64=128$$

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.

$$\left(x-8\right)^{2}=128$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{128}$$

Qisqartirish.

$$x-8=8\sqrt{2} x-8=-8\sqrt{2}$$

8 ni tenglamaning ikkala tarafiga qo'shish.

$$x=8\sqrt{2}+8 x=8-8\sqrt{2}$$