0=x^2+12x-18 eching

$$0 = x ^ { 2 } + 12 x - 18$$

x uchun yechish

$$x=3\sqrt{6}-6\approx 1,348469228$$

$$x=-3\sqrt{6}-6\approx -13,348469228$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+12x-18=0$$

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 -18 ni c bilan almashtiring.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-18\right)}}{2}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\left(-18\right)}}{2}$$

-4 ni -18 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+72}}{2}$$

144 ni 72 ga qo'shish.

$$x=\frac{-12±\sqrt{216}}{2}$$

216 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±6\sqrt{6}}{2}$$

x=\frac{-12±6\sqrt{6}}{2} tenglamasini yeching, bunda ± musbat. -12 ni 6\sqrt{6} ga qo'shish.

$$x=\frac{6\sqrt{6}-12}{2}$$

-12+6\sqrt{6} ni 2 ga bo'lish.

$$x=3\sqrt{6}-6$$

x=\frac{-12±6\sqrt{6}}{2} tenglamasini yeching, bunda ± manfiy. -12 dan 6\sqrt{6} ni ayirish.

$$x=\frac{-6\sqrt{6}-12}{2}$$

-12-6\sqrt{6} ni 2 ga bo'lish.

$$x=-3\sqrt{6}-6$$

Tenglama yechildi.

$$x=3\sqrt{6}-6 x=-3\sqrt{6}-6$$

Kvadratni yakunlash bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}+12x-18=0$$

18 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$x^{2}+12x=18$$

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.

$$x^{2}+12x+6^{2}=18+6^{2}$$

6 kvadratini chiqarish.

$$x^{2}+12x+36=18+36$$

18 ni 36 ga qo'shish.

$$x^{2}+12x+36=54$$

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.

$$\left(x+6\right)^{2}=54$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{54}$$

Qisqartirish.

$$x+6=3\sqrt{6} x+6=-3\sqrt{6}$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$x=3\sqrt{6}-6 x=-3\sqrt{6}-6$$