x^2+67=18x eching

$$x ^ { 2 } + 67 = 18 x$$

x uchun yechish

$$x=\sqrt{14}+9\approx 12,741657387$$

$$x=9-\sqrt{14}\approx 5,258342613$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 18x ni ayirish.

$$x^{2}+67-18x=0$$

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.

$$x^{2}-18x+67=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -18 ni b va 67 ni c bilan almashtiring.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 67}}{2}$$

-18 kvadratini chiqarish.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 67}}{2}$$

-4 ni 67 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324-268}}{2}$$

324 ni -268 ga qo'shish.

$$x=\frac{-\left(-18\right)±\sqrt{56}}{2}$$

56 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-18\right)±2\sqrt{14}}{2}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±2\sqrt{14}}{2}$$

x=\frac{18±2\sqrt{14}}{2} tenglamasini yeching, bunda ± musbat. 18 ni 2\sqrt{14} ga qo'shish.

$$x=\frac{2\sqrt{14}+18}{2}$$

18+2\sqrt{14} ni 2 ga bo'lish.

$$x=\sqrt{14}+9$$

x=\frac{18±2\sqrt{14}}{2} tenglamasini yeching, bunda ± manfiy. 18 dan 2\sqrt{14} ni ayirish.

$$x=\frac{18-2\sqrt{14}}{2}$$

18-2\sqrt{14} ni 2 ga bo'lish.

$$x=9-\sqrt{14}$$

Tenglama yechildi.

$$x=\sqrt{14}+9 x=9-\sqrt{14}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 18x ni ayirish.

$$x^{2}+67-18x=0$$

Ikkala tarafdan 67 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-18x=-67$$

-18 ni bo‘lish, x shartining koeffitsienti, 2 ga -9 olish uchun. Keyin, -9 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-18x+\left(-9\right)^{2}=-67+\left(-9\right)^{2}$$

-9 kvadratini chiqarish.

$$x^{2}-18x+81=-67+81$$

-67 ni 81 ga qo'shish.

$$x^{2}-18x+81=14$$

x^{2}-18x+81 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-9\right)^{2}=14$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{14}$$

Qisqartirish.

$$x-9=\sqrt{14} x-9=-\sqrt{14}$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{14}+9 x=9-\sqrt{14}$$