x^2=12x+17 eching

$$x ^ { 2 } = 12 x + 17$$

x uchun yechish

$$x=\sqrt{53}+6\approx 13,280109889$$

$$x=6-\sqrt{53}\approx -1,280109889$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 12x ni ayirish.

$$x^{2}-12x=17$$

Ikkala tarafdan 17 ni ayirish.

$$x^{2}-12x-17=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -12 ni b va -17 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-17\right)}}{2}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-17\right)}}{2}$$

-4 ni -17 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+68}}{2}$$

144 ni 68 ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{212}}{2}$$

212 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±2\sqrt{53}}{2}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±2\sqrt{53}}{2}$$

x=\frac{12±2\sqrt{53}}{2} tenglamasini yeching, bunda ± musbat. 12 ni 2\sqrt{53} ga qo'shish.

$$x=\frac{2\sqrt{53}+12}{2}$$

12+2\sqrt{53} ni 2 ga bo'lish.

$$x=\sqrt{53}+6$$

x=\frac{12±2\sqrt{53}}{2} tenglamasini yeching, bunda ± manfiy. 12 dan 2\sqrt{53} ni ayirish.

$$x=\frac{12-2\sqrt{53}}{2}$$

12-2\sqrt{53} ni 2 ga bo'lish.

$$x=6-\sqrt{53}$$

Tenglama yechildi.

$$x=\sqrt{53}+6 x=6-\sqrt{53}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 12x ni ayirish.

$$x^{2}-12x=17$$

-12 ni bo‘lish, x shartining koeffitsienti, 2 ga -6 olish uchun. Keyin, -6 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-12x+\left(-6\right)^{2}=17+\left(-6\right)^{2}$$

-6 kvadratini chiqarish.

$$x^{2}-12x+36=17+36$$

17 ni 36 ga qo'shish.

$$x^{2}-12x+36=53$$

x^{2}-12x+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-6\right)^{2}=53$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-6\right)^{2}}=\sqrt{53}$$

Qisqartirish.

$$x-6=\sqrt{53} x-6=-\sqrt{53}$$

6 ni tenglamaning ikkala tarafiga qo'shish.

$$x=\sqrt{53}+6 x=6-\sqrt{53}$$