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

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

x uchun yechish

$$x=-8$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(-\frac{1}{2}x-4\right)=0$$

Tenglamani yechish uchun x=0 va -\frac{x}{2}-4=0 ni yeching.

$$x=0 x=-8$$

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.

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

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

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

\left(-4\right)^{2} ning kvadrat ildizini chiqarish.

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

-4 ning teskarisi 4 ga teng.

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

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

$$x=\frac{4±4}{-1}$$

x=\frac{4±4}{-1} tenglamasini yeching, bunda ± musbat. 4 ni 4 ga qo'shish.

$$x=\frac{8}{-1}$$

8 ni -1 ga bo'lish.

$$x=-8$$

x=\frac{4±4}{-1} tenglamasini yeching, bunda ± manfiy. 4 dan 4 ni ayirish.

$$x=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-8 x=0$$

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.

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

Ikkala tarafini -2 ga ko‘paytiring.

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

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

$$x^{2}+\left(-\frac{4}{-\frac{1}{2}}\right)x=\frac{0}{-\frac{1}{2}}$$

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

$$x^{2}+8x=\frac{0}{-\frac{1}{2}}$$

0 ni -\frac{1}{2} ga bo'lish 0 ga k'paytirish -\frac{1}{2} ga qaytarish.

$$x^{2}+8x=0$$

8 ni bo‘lish, x shartining koeffitsienti, 2 ga 4 olish uchun. Keyin, 4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+8x+4^{2}=4^{2}$$

4 kvadratini chiqarish.

$$x^{2}+8x+16=16$$

x^{2}+8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+4\right)^{2}=16$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{16}$$

Qisqartirish.

$$x+4=4 x+4=-4$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x=0 x=-8$$