x^2-18x-18=-7 eching

$$x ^ { 2 } - 18 x - 18 = - 7$$

x uchun yechish

$$x=2\sqrt{23}+9\approx 18,591663047$$

$$x=9-2\sqrt{23}\approx -0,591663047$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$x^{2}-18x-18=-7$$

7 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-18x-18-\left(-7\right)=-7-\left(-7\right)$$

O‘zidan -7 ayirilsa 0 qoladi.

$$x^{2}-18x-18-\left(-7\right)=0$$

-18 dan -7 ni ayirish.

$$x^{2}-18x-11=0$$

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 -11 ni c bilan almashtiring.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\left(-11\right)}}{2}$$

-18 kvadratini chiqarish.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\left(-11\right)}}{2}$$

-4 ni -11 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324+44}}{2}$$

324 ni 44 ga qo'shish.

$$x=\frac{-\left(-18\right)±\sqrt{368}}{2}$$

368 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-18\right)±4\sqrt{23}}{2}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±4\sqrt{23}}{2}$$

x=\frac{18±4\sqrt{23}}{2} tenglamasini yeching, bunda ± musbat. 18 ni 4\sqrt{23} ga qo'shish.

$$x=\frac{4\sqrt{23}+18}{2}$$

18+4\sqrt{23} ni 2 ga bo'lish.

$$x=2\sqrt{23}+9$$

x=\frac{18±4\sqrt{23}}{2} tenglamasini yeching, bunda ± manfiy. 18 dan 4\sqrt{23} ni ayirish.

$$x=\frac{18-4\sqrt{23}}{2}$$

18-4\sqrt{23} ni 2 ga bo'lish.

$$x=9-2\sqrt{23}$$

Tenglama yechildi.

$$x=2\sqrt{23}+9 x=9-2\sqrt{23}$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}-18x-18=-7$$

18 ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-18x-18-\left(-18\right)=-7-\left(-18\right)$$

O‘zidan -18 ayirilsa 0 qoladi.

$$x^{2}-18x=-7-\left(-18\right)$$

-7 dan -18 ni ayirish.

$$x^{2}-18x=11$$

-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.

$$x^{2}-18x+\left(-9\right)^{2}=11+\left(-9\right)^{2}$$

-9 kvadratini chiqarish.

$$x^{2}-18x+81=11+81$$

11 ni 81 ga qo'shish.

$$x^{2}-18x+81=92$$

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.

$$\left(x-9\right)^{2}=92$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{92}$$

Qisqartirish.

$$x-9=2\sqrt{23} x-9=-2\sqrt{23}$$

9 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2\sqrt{23}+9 x=9-2\sqrt{23}$$