-1/2x^2+4-x=0 eching

$$- \frac { 1 } { 2 } x ^ { 2 } + 4 - x = 0$$

x uchun yechish

$$x=-4$$

$$x=2$$

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.

$$-\frac{1}{2}x^{2}-x+4=0$$

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 4 ni c bilan almashtiring.

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

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

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

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+8}}{2\left(-\frac{1}{2}\right)}$$

1 ni 8 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{9}}{2\left(-\frac{1}{2}\right)}$$

9 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±3}{2\left(-\frac{1}{2}\right)}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±3}{2\left(-\frac{1}{2}\right)}$$

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

$$x=\frac{1±3}{-1}$$

x=\frac{1±3}{-1} tenglamasini yeching, bunda ± musbat. 1 ni 3 ga qo'shish.

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

4 ni -1 ga bo'lish.

$$x=-4$$

x=\frac{1±3}{-1} tenglamasini yeching, bunda ± manfiy. 1 dan 3 ni ayirish.

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

-2 ni -1 ga bo'lish.

$$x=2$$

Tenglama yechildi.

$$x=-4 x=2$$

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.

$$-\frac{1}{2}x^{2}-x+4=0$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$-\frac{1}{2}x^{2}-x+4-4=-4$$

O‘zidan 4 ayirilsa 0 qoladi.

$$-\frac{1}{2}x^{2}-x=-4$$

Ikkala tarafini -2 ga ko‘paytiring.

$$\frac{-\frac{1}{2}x^{2}-x}{-\frac{1}{2}}=-\frac{4}{-\frac{1}{2}}$$

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

$$x^{2}+\left(-\frac{1}{-\frac{1}{2}}\right)x=-\frac{4}{-\frac{1}{2}}$$

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

$$x^{2}+2x=-\frac{4}{-\frac{1}{2}}$$

-4 ni -\frac{1}{2} ga bo'lish -4 ga k'paytirish -\frac{1}{2} ga qaytarish.

$$x^{2}+2x=8$$

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.

$$x^{2}+2x+1^{2}=8+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=8+1$$

8 ni 1 ga qo'shish.

$$x^{2}+2x+1=9$$

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.

$$\left(x+1\right)^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{9}$$

Qisqartirish.

$$x+1=3 x+1=-3$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=2 x=-4$$