1/2x^2+x-12=0 eching

$$\frac { 1 } { 2 } x ^ { 2 } + x - 12 = 0$$

x uchun yechish

$$x=-6$$

$$x=4$$

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.

$$\frac{1}{2}x^{2}+x-12=0$$

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

$$x=\frac{-1±\sqrt{1^{2}-4\times \frac{1}{2}\left(-12\right)}}{2\times \frac{1}{2}}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\times \frac{1}{2}\left(-12\right)}}{2\times \frac{1}{2}}$$

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

$$x=\frac{-1±\sqrt{1-2\left(-12\right)}}{2\times \frac{1}{2}}$$

-2 ni -12 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+24}}{2\times \frac{1}{2}}$$

1 ni 24 ga qo'shish.

$$x=\frac{-1±\sqrt{25}}{2\times \frac{1}{2}}$$

25 ning kvadrat ildizini chiqarish.

$$x=\frac{-1±5}{2\times \frac{1}{2}}$$

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

$$x=\frac{-1±5}{1}$$

x=\frac{-1±5}{1} tenglamasini yeching, bunda ± musbat. -1 ni 5 ga qo'shish.

$$x=\frac{4}{1}$$

4 ni 1 ga bo'lish.

$$x=4$$

x=\frac{-1±5}{1} tenglamasini yeching, bunda ± manfiy. -1 dan 5 ni ayirish.

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

-6 ni 1 ga bo'lish.

$$x=-6$$

Tenglama yechildi.

$$x=4 x=-6$$

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.

$$\frac{1}{2}x^{2}+x-12=0$$

12 ni tenglamaning ikkala tarafiga qo'shish.

$$\frac{1}{2}x^{2}+x-12-\left(-12\right)=-\left(-12\right)$$

O‘zidan -12 ayirilsa 0 qoladi.

$$\frac{1}{2}x^{2}+x=-\left(-12\right)$$

0 dan -12 ni ayirish.

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

Ikkala tarafini 2 ga ko‘paytiring.

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

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

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

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

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

12 ni \frac{1}{2} ga bo'lish 12 ga k'paytirish \frac{1}{2} ga qaytarish.

$$x^{2}+2x=24$$

2 ni bo‘lish, x shartining koeffitsienti, 2 ga 1 olish uchun. Keyin, 1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+2x+1^{2}=24+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=24+1$$

24 ni 1 ga qo'shish.

$$x^{2}+2x+1=25$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+1\right)^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{25}$$

Qisqartirish.

$$x+1=5 x+1=-5$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=4 x=-6$$