1/2x^2+6x+18=0 eching

$$\frac { 1 } { 2 } x ^ { 2 } + 6 x + 18 = 0$$

x uchun yechish

$$x=-6$$

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.

$$\frac{1}{2}x^{2}+6x+18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} \frac{1}{2} ni a, 6 ni b va 18 ni c bilan almashtiring.

$$x=\frac{-6±\sqrt{6^{2}-4\times \frac{1}{2}\times 18}}{2\times \frac{1}{2}}$$

6 kvadratini chiqarish.

$$x=\frac{-6±\sqrt{36-4\times \frac{1}{2}\times 18}}{2\times \frac{1}{2}}$$

-4 ni \frac{1}{2} marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-2\times 18}}{2\times \frac{1}{2}}$$

-2 ni 18 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-36}}{2\times \frac{1}{2}}$$

36 ni -36 ga qo'shish.

$$x=\frac{-6±\sqrt{0}}{2\times \frac{1}{2}}$$

0 ning kvadrat ildizini chiqarish.

$$x=-\frac{6}{2\times \frac{1}{2}}$$

2 ni \frac{1}{2} marotabaga ko'paytirish.

$$x=-\frac{6}{1}$$

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.

$$\frac{1}{2}x^{2}+6x+18=0$$

Tenglamaning ikkala tarafidan 18 ni ayirish.

$$\frac{1}{2}x^{2}+6x+18-18=-18$$

O‘zidan 18 ayirilsa 0 qoladi.

$$\frac{1}{2}x^{2}+6x=-18$$

Ikkala tarafini 2 ga ko‘paytiring.

$$\frac{\frac{1}{2}x^{2}+6x}{\frac{1}{2}}=-\frac{18}{\frac{1}{2}}$$

\frac{1}{2} ga bo'lish \frac{1}{2} ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{6}{\frac{1}{2}}x=-\frac{18}{\frac{1}{2}}$$

6 ni \frac{1}{2} ga bo'lish 6 ga k'paytirish \frac{1}{2} ga qaytarish.

$$x^{2}+12x=-\frac{18}{\frac{1}{2}}$$

-18 ni \frac{1}{2} ga bo'lish -18 ga k'paytirish \frac{1}{2} ga qaytarish.

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

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.

$$x^{2}+12x+6^{2}=-36+6^{2}$$

6 kvadratini chiqarish.

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

-36 ni 36 ga qo'shish.

$$x^{2}+12x+36=0$$

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.

$$\left(x+6\right)^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{0}$$

Qisqartirish.

$$x+6=0 x+6=0$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$x=-6 x=-6$$

Tenglama yechildi. Yechimlar bir xil.

$$x=-6$$